The former England midfielder arrives at the Vitality Stadium after agreeing to a mutual termination of his contract at Craven Cottage and will replace Jonathan Woodgate, who left his role as interim Bournemouth manager on Sunday.
Parker was initially appointed as an interim Fulham manager in February 2019 but could not prevent them from getting relegated to the Championship.
Following his permanent appointment in the summer of 2019, Parker returned Fulham to the Premier League in his first full season in charge but the Cottagers finished 18th in the top flight last season, making another swift return to the second tier.
"I believe this is the perfect fit for both parties," Parker told AFCBTV following his appointment.
"I'm familiar with Bournemouth because of my relationship with Harry Arter. It's a football club I know well from watching him over the years.
"The ethos, the reputation, the journey and the challenge here is something that's very exciting for me and my staff. We want to build a team the fans can be proud of and one they feel represents them. We can't wait to get started."
Bournemouth chief executive Neill Blake said: "It has been a long process but I am delighted to finally get our man.
"Scott has always been our number one choice for this role and someone whose coaching career we have taken a keen interest in since his first steps in Tottenham Hotspur's academy.
"Over a period of time he has proven himself as one of the best young head coaches in the country; someone who has a clear philosophy on how he wants to play and knows what it takes to win promotion from the Championship.
"Scott is fully invested in the long-term project in front of us here, and this is the start of an exciting new period for this club."
