Riley said in a statement: "While I am disappointed by LeBron's decision to leave Miami, no-one can fault another person for wanting to return home.
"The last four years have been an incredible run for South Florida, Heat fans, our organisation and for all of the players who were a part of it. LeBron is a fantastic leader, athlete, teammate and person, and we are all sorry to see him go.
"We've won multiple championships and competed for many others. Micky [Arison], Erik [Spoelstra] and I remain committed to doing whatever it takes to win and compete for championships for many years to come. We've proven that we can do it and we'll do it again."
The Heat won two NBA titles during James's four-year spell with the team.