At Vox.com Matthew Yglesias conributes the most credible explaination yet offered why Sen. Bernie Sanders will surely support Hillary Clinton, if she wins the Democratic nomination:

…Sanders already has all the reasons he could possibly need to give Clinton his full-throated support.
Thanks to the primaries, Sanders has emerged as a substantial factional leader inside the Democratic Party — someone whose statements and tweets will garner media attention, whose email list will be coveted and envied by other Democrats in Congress, and whose support or opposition to a measure will matter to a national constituency. That gives him, potentially, considerably more influence over national affairs than he’s had in his previous 25 years in Washington. But essentially all of that influence hinges on Clinton winning the election in November.
That, rather than anything to do with platform concessions or “lesser of two evils” talk, is why Sanders will almost certainly do everything in his power to boost Clinton this fall. He’ll do it because it’s the right thing for Bernie Sanders.

Their differences on key issues are more a matter of degree than substance, as Yglesias notes,

Clinton and Sanders are pulling in the same direction on almost every issue.
Sanders wants to raise the federal minimum wage from $7.25 an hour to $15 an hour; Clinton wants $12.
Sanders wants a massive increase in taxes on the wealthy; Clinton wants a modest one.
Sanders wants a big new government-run health insurance program to cover everyone; Clinton wants to expand an existing government-run insurance program to cover more people.
Sanders wants a hard cap on bank size and complexity; Clinton wants enhanced capital requirements for large and complex banks that would discourage size and complexity.

Yglesias adds, “…On virtually every issue, Sanders has promised to go further than Clinton has in the same direction. Which is another way of saying that implementing Clinton’s agenda would be a way of moving closer to Sanders’s goals — so in pursuit of his goals, he’s going to want to put her in the White House.”
In addition, argues Yglesias, a Clinton victory gives Sanders substantially enhanced clout as the leader of a bona fide grass roots movement that has the ear of the President. It would give Sanders inside leverage, as opposed to being the leader of a movement on the outside.
Further, it would give Sanders the inside track to become the chair of one of the most powerful Senate panels, the Health, Education, Labor, and Pensions Committee, with “influence over legislation, of course, but also the ability to call hearings on whatever subject he likes.” That’s a lot better than being a minority member of the committee headed by a Republican, which would likely accompany a Trump victory.
Sanders is a pragmatic progressive, not a Naderesque ideologue who would rather go down in a blaze of purist glory than support reforms that can benefit millions of working people. Sanders is not giving up his efforts to win an upset victory. But he clearly understands that a Clinton presidency would provide support for his policy reforms, support that would be completely denied by Republican control of the Senate. For both moral and practical reasons, he will work hard to elect the Democratic presidential nominee, as will most of his supporters.