It's the first time Young has addressed months of speculation that he and Hannah tied the knot over the summer.
Young was previously married to singer-songwriter Pegi Young but the two divorced in 2014.
Rumours began circulating in August when Hannah's Instagram page filled with comments congratulating her on the ceremony.
Once he began dating Hannah the two spent ample time working on projects together.
Young also wrote the soundtrack for the film that premiered this year at the South By South West Festival.
The video encourages Americans to vote in the midterm elections, saying there are "no real laws protecting us from guns, and...politicians supporting the NRA because the NRA supports them".
Written in 1970, Ohio is a protest song in reaction to the Kent State shootings which saw four unarmed anti-war students shot dead by members of the Ohio National Guard.
"It was a pivotal moment for me", he wrote.
In the online message entitled, "Again", the 72-year-old star refers to Hannah as '"my wife Daryl" and goes on to talk about the video, shared with the message, they put together which advocates for student protection against gun violence and achieving more gun laws to "protect our people". "Today's students are courageous, demanding change in violent times", he wrote. "Not more guns", he said.
"Give us common sense gun laws that protect our people, in schools, in places of worship, in the workplace and on the streets".