The former midfielder - who first took over with Fulham on the brink of Premier League relegation in 2019 - could not save the Cottagers from dropping back into the Championship last season, having led them back into the top-flight through the Play-Offs during his first full season in charge.
There have been tensions between Parker and owner Shahid Khan, as well as Khan's son, Tony, the director of football, which have contributed to his mutual termination.
In a statement on Monday, Fulham said: "Fulham Football Club can confirm that Scott Parker has left the Club by mutual consent."
Parker has since been appointed as manager of Bournemouth, taking over from Jonathan Woodgate, who replaced Jason Tindall in February and could only guide the Cherries to the Play-Off semi-finals.
A sizeable number of backroom staff have followed Parker out of Craven Cottage, with Matt Wells (first-team coach), Rob Burch (goalkeeping coach), Alastair Harris (head of sports science), Jonathan Hill (first-team match analyst) and Charlie Moore (lead physical performance coach) also departing.
Swansea manager Steve Cooper, who was considered by Crystal Palace, is a leading contender to replace Parker in west London.
Fulham chairman Khan said: "Through promotion and relegation alike, Scott has always enjoyed my support as our Head Coach.
“Scott’s departure does nothing to shake my confidence, however. We will hire a new Head Coach who is capable of achieving our goal of promotion and will be committed to Fulham and its supporters. And we will field a squad that will respond, compete and win. Onward.”