James Madison, over the last several years, had been a key figure in shaping GW's political views; he joined with James Monroe and Edmund Randolph in pressing GW to re-enter politics, since the Constitutional Convention scheduled in Philadelphia in May, 1787.
Shays' Rebellion (1786-1787) was perhaps the most useful crisis in U.S. History. The rebellion horrified GW, and his letters show much more political agitation than what he showed on the surface. Shays' Rebellion also crystallized GW's belief that the Articles of Confederation had to be replaced with a stronger national government . . . his days as a Virginia Planter at Mount Vernon were yet again numbered.
Henry Knox (GW's artillery officer during the Revolution) made GW's decision for him: in a personal letter, Knox argued that if GW didn't go to Philadelphia and the convention failed, it would forever harm GW's reputation in history. But, if GW presided over the convention, and a strong federal government was the result, then GW would become even greater in the present, and more-so in history.
The Virginia delegation became a cohesive group, meeting for 2 to 3 hours a day until the convention was able to officially begin. On 25 May, 1787, the convention finally had seven state delegations, and GW was unanimously elected President of the convention.
The role of President was ideal for GW, in that the position was officially nonpartisan and nonspeaking while in session (He would have plenty to say when the convention was out of session). GW was not an "Originator", but a keen judge of the points-of-view and arguments from others; it also greatly benefited GW that others framed the debate during the convention. GW's mere presence guaranteed that the Constitutional Convention was at least perceived as striving for the public good.
For the most part, the delegates at the convention were motivated and governed by their hopes rather than their fears, which was largely attributed to the presence of GW. Also, GW was the reason why each member of the House of Representatives was based on 30,000 citizens. Despite not getting all he wanted in the final draft, he was a strong supporter of the proposed Constitution; he put his trust in the amendment process to refine any imperfections contained in the document.
As the newly "elected" President, GW didn't see himself finishing the first term; he figured in two years, he would be back at Mount Vernon . . . he never envisioned eight long years as President. Had GW known his commitment would have been that long, he never would have agreed to be the nation's first Chief Executive.
(Below: the results of the "Election" of 1789 - side note: John Adams was appalled that he didn't even receive anything close to half the Electoral Votes, such was his view of his level of importance at this time in U.S. History)