Henderson, who had the option to leave Old Trafford on a free transfer this summer, was reportedly being tracked by Bristol City and Stoke City.
The England Under-21 stopper, who spent last season on loan at Shrewsbury Town, has ended speculation surrounding his future by extending his stay in Greater Manchester until 2020, in a deal that also offers the option of an extra year.
"I'm really delighted," Henderson told MUTV. "Coming off the back of last season and playing games at Shrewsbury and having a good season there, to return to the biggest club in the world and put pen-to-paper again is a great achievement for me and my family. It's another dream come true.
"Obviously, there was a lot of interest after last season, when I've done myself well going out and playing but, look, United are the biggest club in the world and have been my club since day one so, of course, they are always first in my mind.
"All my family are here with me now and it's an honour. To come from where we started from, from nothing, to come all this way is fantastic and I'm just really delighted."
Henderson, who appeared 10 times for Shrewsbury last season, also has one cap with the Three Lions Under-21 side.