Henderson spent the whole of last season with Salop, playing 48 games.
The 21-year-old was named in the PFA League One team of the season.
“I’m really delighted,” said Henderson.
“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’s form for Town last campaign saw him capped by England’s Under-21s in March, beating Romania 2-1 in a friendly.
Salop are on the lookout for a new shot-stopper after losing him and Craig MacGillivray.