Title really, I was wondering why he chose him over more well known possible successors like Speer, Goring, etc.
On April 22nd, 1945, Hitler announced his intent to stay in Berlin to see through the end of the war, and that he planned on committing suicide rather than be captured by the Red Army. Hermann Göring then dug up a succession law that said if Hitler didn't have capacity to govern, he would become acting Führer. He sent a telegram to the Führerbunker saying that if he didn't hear otherwise from Hitler by 10 PM of April 24th, he'd assume Hitler was incapacitated and invoke the law. Hitler was furious, his anger stoked by Party Chancellery leader Martin Bormann, and sent a reply the next day demanding that Göring resign; he was placed under house arrest by the SS shortly after.
Meanwhile, Heinrich Himmler had entered into clandestine negotiations through Count Folke Bernadotte (nephew of the King of Sweden), claiming that he had provisional leadership power to negotiate terms of surrender. He even used the liberation of concentration camp prisoners to buy himself goodwill with the western Allies. Unsurprisingly, Hitler was furious again, denouncing it as the "most shameful betrayal in human history." He ordered Himmler arrested, and had the highest-ranking SS subordinate—Hermann Fegelein, Eva Braun's brother-in-law who had previously tried to escape the Führerbunker in civilian clothes—executed.
When Hitler drafted his will on April 29th, he had listed Goebbels and Dönitz—essentially the two most high-ranking officials he still trusted—as Chancellor and President, respectively. Bormann would remain in his role in the Party Chancellery. The will notably contained a clause that officially stripped Goering of all his ranks and expelled him from the Nazi Party. Hitler hoped Goebbels would leave Berlin, and Goebbels didn't announce his intent to commit suicide until after Hitler's death.
(Source: Richard Evans, The Third Reich at War)