"I couldn't be happier. When I came back to the club on loan in February I was hoping that it might lead to something permanent," he told Forest's official website.
"I believe we're heading for big things next season with new players coming in and David Johnson fit again,"
"I've thoroughly enjoyed being back here and in many ways it has been like returning home after spending so many happy times here before."
Rogers was previously at the City Ground between 1997 and 2001.