Nelson started 16 games the past two seasons at Minnesota, including nine in 2013. However, two weeks ago he announced he was leaving the school in order to seek a more pass-oriented offense.
On Tuesday, ESPN reported that former Maryland coach Ralph Friedgen would become the Scarlet Knights' offensive coordinator.
Players transferring within the Big Ten normally lose a year of eligibility. But because Rutgers does not officially join the league until July 1, Nelson still will have two years of eligibility remaining after sitting out 2014 under NCAA transfer rules.
CBSSports.com first reported Nelson was headed to Rutgers.
Nelson completed 50.5 percent of his passes last season for 1,306 yards and nine touchdowns, with six interceptions.
Information from ESPN.com's Brian Bennett was used in this report.