The midfielder began last season as Reds skipper but suffered an injury-hit campaign as Town were eventually relegated.
New boss Mark Yates also revealed he has withdrawn contract offers to midfield duo Marvin Elliott and Dean Morgan.
Yates said: “Josh Simpson has turned us down. He wants to look at other options which we fully understand and we wish Josh all the best for the future.
“He has been a great servant of Crawley Town over the last four years and he will always be a welcome visitor to the club.
“We are pleased that Bobson Bawling has agreed a new one-year deal and we are still in discussions with Conor Henderson.
“The club initially made offers to Marvin Elliott and Dean Morgan but after evaluating the squad I decided not to go any further with these two players. I would like to thank both for their services to the club and wish them all the best for the future.”
Town have also released Brian Jensen, Dean Leacock, Charles Banya, Emmett O’Connor, Blair Anderson, Bradley Isaacs, Kelly Youga, John Cofie and Ryan Richefond at the end of their contracts.