Alongside a photograph of the happy couple signing the marriage register, Stephen wrote: "Gosh. @ElliottGSpencer and I go into a room as two people, sign a book and leave as one. Amazing. (sic)"
The couple made a formal application to marry at a register office in Dereham, Norfolk - the comedian's home county - on December 23rd.
Meanwhile, Stephen - who has suffered with depression for years - has reportedly "found new hope" after starting to date his now-husband.
A friend of the star previously said: "Since Stephen met Elliott it is like he has a new lust for life.
"We've got the old Stephen back. He has spoken about his problems in the past because he wants others suffering with depression and loneliness to know it can affect everyone.
"But he has found new hope in Elliott and they thrive off one another."