Thomson is 150 miles west of Chicago, near the border with Iowa.
The governor said Thomson would be maximum security federal prison, and he stressed that no one has ever escaped from such a facility.
"It is worth a lot of jobs to our state. If Thomson Prison is sold to the federal government, it'll bring 3,200 new jobs, and about a billion dollars of new income. So part of the deal is we've got to get our economy back on track. If Illinois can get a federal prison, maximum security, that is something that's worth fighting for," said Quinn.
Quinn said the prison is now almost vacant.