Whiting had been on a two-month loan deal with the Centurions, making 8 appearances after finding his chances at Hull FC limited given their off-season recruitment.
The 31 year-old had made 278 appearances for the Black and Whites during his 12 years at the club, being granted a testimonial year in 2014 for his services to Hull FC.
Leigh Centurions head coach Neil Jukes has said he is delighted to acquire the services of someone with such experience and quality.
“Richard is a great professional and has proved himself to be a big asset during his time with us,” Jukes told the club’s official website.
“He is a very versatile player and has really enjoyed his time here. I know that in one way he will be sad to leave Hull after giving many years of valuable service to them but he is excited by the challenge at Leigh Centurions and ready to write a new chapter into his illustrious playing career.
“When he first joined us I said he hadn’t joined us as a stop-gap but was a player of genuine quality who came highly recommended as a top professional who was low maintenance.
“He quickly adapted to being at our Club and through working hard and buying in to what we want to achieve we now have an end result that suits all parties.”