This is one of those questions that has both relatively succinct, and incredibly long answers.

In short, he invaded when he did because the King of England, Edward, had just died and left no heir or instructions for his succession. This left three potential kings, one of whom was very quickly elected as king by the Anglo-Saxon nobility, forcing the other two to invade before he solidified his rule.

The longer (but still relatively concise) story goes like this:

We'll start with Æthelred the Unready, who ruled England from 978 to 1013 and again from 1014 to 1016. His second wife was Emma of Normandy, the sister of Richard II, Duke of Normandy. This is where the Dukes of Normandy are first connected with the Kings of England. Æthelred's son with Emma, his seventh son in total, was Edward (the Confessor).

Fast-forward to the early 1030s. Cnut, the King of Denmark, has conquered England and married Æthelred's widow, Emma of Normandy. Edward is the now eldest surviving son of Æthelred and is living in exile in Normandy with his mother's family.

In 1034, Duke Robert I of Normandy attempted to put Edward on the throne of England but the ships were blown off course. Edward tried again in 1036 - after Cnut died - but this only results in his younger brother Alfred being blinded and killed and Edward retreating back to Normandy.

In 1041 the King of England, Harthacnut, who is the son of Cnut and Emma of Normandy (so Edward's half-brother) invited Edward back to England to be his heir. He was sworn in and, when Harthacnut died in 1042, Edward - with the support of the most powerful Anglo-Saxon nobles - ascended to the throne.

With Edward on the throne of England there was a strong connection to Normandy. Not only was his mother related to the Duke of Normandy, but he spent most of his life there and he received significant material support from the Duke. He placed many Normans in positions of power and prestige. This Norman influence led to Edward's father-in-law Godwin, the Earl of Wessex (and one of the most powerful nobles in England), leading a faction in opposition to Norman influence.

Edward died in 1066 with no heir, leaving three people with strong claims.

The first was Harold Godwinson. Harold had taken his father's position as the most powerful noble in England and the head of an anti-Norman opposition. He claimed that Edward had entrusted the kingdom to his "protection" on his deathbed. He was selected by the Witenagemot (the collection of Anglo-Saxon nobles) as king and crowned days after Edward's death.

The second was Harald Hardrada, the King of Norway. His claim was based on an agreement between King Harthacnut and King Magnus of Norway that if either died without heir, the other would inherit both kingdoms.

The third was William, Duke of Normandy. William claimed that he had been promised the kingship by Edward (which may well be true) and that Harold Godwinson had sworn to support this. Upon finding out that Harold had been crowned, William began assembling an invasion fleet to take what he saw as his.

So, to sum up, the kingship of England had been tumultuous for a while and, even while Edward lived, there were pro-Norman and anti-Norman factions. With his heir-less death the anti-Norman faction was able to quickly capitalize on this and Harold Godwinson took over as king. Throw in a Norman with a good claim to the throne (and a proven skill in battle) and a foreign king with a decent claim and you now have the stage set for the Norman conquest.