Beijing is one of China's 中国四大古都, "Four Ancient Great Capitals." The other three are Nanjing, Luoyang, and Xi'an, respectively. And funnily enough, of those four, only Nanjing is near a navigable, natural waterway. (There have subsequently been added four other "traditional" capitals as of the 20th century, namely: Kaifeng, Hangzhou, Anyang, and Zhengzhou).
What is today known as Beijing has gone by quite a few names over the centuries, but the site has seen continuous settlement for at least 3,000 years, and has served as a regional capital since at least the Warring States period of the 4th c. BCE of the states of Ji and Yan, respectively, then called Jicheng (蓟城, "Thistle Town"). Later on during the Eastern Han Dynasty (25-220 CE) it served as a provincial capital of Youzhou.
It remained more or less as-such during the early imperial era, through the Qin and Han Dynasties, up until the Sui and Tang of the 7th century. The Sui Emperors (all 2 of them) worked their populace to the bone ordering the construction of the Grand Canal network that would link the Yellow and Yangtze Rivers, and also provide an easily navigable water route to the then-capital, Chang'an (Xi'an). But a secondary purpose for the Canals was to more easily move tons of men and material to the Sui emperors' conquest du jour: the Korean kingdom of Goguryeo. And the northernmost terminal of the canal network? You guessed it, Beijing - or as it was known by that point Youzhou (幽州, "Quietville"). The war, incidentally, did not go well for China... by it's end 3 Chinese armies and the Sui Dynasty had all been destroyed, and Goguryeo stood fast... and it would be up to their successor, the Tang Dynasty, to finish the job)
But even though it was now a bustling hub thanks to its new status as canal terminal, it wouldn't be until the 10th-13th centuries when the Khitan of Mongolia/Manchuria formed the Liao Dynasty while the rest of China roiled under one of its periodic breakups (the 5 Dynasties and 10 Kingdoms). The Liao didn't designate Beijing as its primary capital (that was Shangjing, (上京，"The Over-Capital"), but did have it as something of a sub-capital. Rather ironically given its current name (北京，"North Capital") the Liao renamed the city Nanjing (南京, "South Capital)... for reference, modern Nanjing was then called Jiangning (江寧, "[Yangtze] River's Peace")... confusing, I know, just roll with it.
The Jurchen people established the Jin Dynasty in the 12th century, supplanting the Liao in the north, and moving the capital from Shangjing to Beijing, which they first called Yangjing (燕京, "Yan [State] Capital), but then renamed it to Zhongdu (中都, "The All-Center").
Then came the Mongols, who - as is tradition - absolutely steamrolled everything, crushed the Jin as well as Xi Xia to the west, and seized control of northern China before launching what would prove to be a century-long war against the Song of the South. And, well, there was already an administrative hub and imperial capital just sitting there*, it'd be irresponsible not to use it! So they did, first bringing the name back to Yangjing before opting to re-rename it to Khanbaliq (汗八里, "City of the Khan", sometimes corrupted to "Cambulac"... yes, I'm looking at you, Marco) but known in Chinese as Dadu (大都, "Grand Capital").
Well now it's the 1360s, and here comes the Ming, and they establish Nanjing as their capital, and are now calling it Nanjing for reals, because it's in the south... and it's their capital. So there. So they can't call Dadu "Grand Capital" anymore, because it's obviously not the capital... and also they sorta burned down the imperial palace when kicking out the Mongols... awkward. But it is in the north, and they do like peaceful things, so they call it Beiping (北平, "Northern Peace"). but then the Yongle fought a civil war with his uncle who was based in Beiping, and after he won decided that he was tired of the south and that he'd like to move to the north - and so Beiping become Beijing, a co-equal capital with Nanjing. And since the old palace had been not-exactly-accidentally burned down, that was a great excuse to build a new palace, which would be more like a city unto itself, and would definitely be forbidden for commoners and foreigners, and so they called it the Forbidden City (紫禁城). And it was pretty awesome... so awesome, in fact, that all the rest of the emperors would use it as their capital right up unil China decided it was tired of emperors and wanted to try something new... like a Republic. Yeah, that's got a nice ring to it.
Well, the Republic was founded by overthrowing the Manchurians who had taken over China in the 1640s and generally made it rather unpleasant to be Chinese, and made everyone get funny haircuts. So when they overthrew the Manchus, they didn't want to have all that imperial stuff around their shiny new republic, so they moved the capital back to Nanjing, and made Beijing go back to being Beiping. But then Mao Zedong and friends were kicked out of the south, and had to go on a rather long march, called The Long March, up to the north. Then the Japanese decided that they'd like to be a part of this party, and came over without an invite, at which point both Mao and Jiang said "hey, no one can pick on my obnoxious brother except me!" But when the Japanese finally went home, Mao (surprise!) kicked Jiang and his Nationalists out of China (almost) entirely, and wanted everyone to know that China was now a republic for the people, a People's Republic... of China. And so no one got confused between Republic and People's Republic, he made sure to move the capital from Nanjing up to where he's set up his base of operations and people generally like him better - back to Beiping, I mean Beijing. But this time they didn't make Nanjing call itself Nanping, they just let it keep it's old name even though it wasn't the capital anymore.
TL;DR: Beijing was the capital of Eastasia: Beijing has always been the capital of Eastasia. It is the capital because it has always been the capital... except when it hasn't been.
Dong, Madeleine Yue (2003). Republican Beijing: The City and Its Histories.
Gaubatz, Piper (1995). "Changing Beijing" in Geographical Review
Beijing was not the initial capital of Ming dynasty. The first capital of Ming dynasty was Nanjing. After taking the throne from his nephew, Yongle moved the capital from Nanjing to Beijing. Beijing was Yongle base. It's easier and safer for him to control the empire if he can operate the empire from his homebase.
By 1400 and onward, water source was no longer factor for a city to grow big although the location of Beijing was indeed not idea for a capital included having no water source in emergency, very close to the northern civilizations and too far away from the southern provinces. This put Beijing in constant danger from northern threats and the southern lords became harder and harder to control.