The former Leeds player was out of contract at the end of the season but has agreed a new 12-month deal.
The news comes just two days after Hull KR announced the capture of Salford centre Sean Gleeson.
Reds director of football Steve Simms said: "Ashley has been a great servant of the club over the past couple of seasons.
"He's a dangerous centre and we are very pleased he shares the coaching staff and directors' vision for where we want to take the club."
Gibson, 25, has scored 28 tries in 55 appearances since joining the Reds from Leeds in 2010.