The much rumoured move was finally agreed on Sunday night with the Celtics receiving a 2015 first-round draft pick for letting Rivers out of his contract, the Globe said, citing league sources.
Rivers, who in nine seasons with the Celtics compiled a 416-305 record and led the team to a record 17th NBA title in 2008 with another trip to the NBA Finals two years later, had three more years worth $21 million remaining on his Boston contract.
The Celtics enjoyed a long run of success under Rivers after they assembled a Big Three when they acquired center Kevin Garnett and shooting guard Ray Allen to join forward Paul Pierce.
Allen left Boston to join the NBA champion Miami Heat last season and the Celtics squad showed signs of age with a rebuilding period looming in the immediate future.
Reports of talks between the two teams surfaced weeks ago, with Garnett's name also mentioned in a possible swap.
The Celtics finished third in the Atlantic Division last season with a 41-40 mark after winning the crown five years in a row and lost to the New York Knicks in the first round of the playoffs.
The Clippers won the Pacific Division with a 56-26 record but were eliminated in the opening round of the playoffs by the Memphis Grizzlies.
Last month, three weeks after their early ouster from the playoffs, the Clippers announced they would not be renewing the contract of coach Vinny Del Negro whose deal was expiring.
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