The move was expected after Sunderland's relegation from the top flight and the 34-year-old revealed his intention on England duty ahead of Saturday's World Cup qualifier against Scotland.
"It's out there, a lot of people obviously knew, I did a medical and said when this is finished and I've had a break, come July everyone will know anyway," Defoe told the BBC.
Defoe scored 18 goals in 29 games in a previous spell at Bournemouth on loan from West Ham United in 2000-01.
(Reporting by Neil Robinson; editing by Ken Ferris)
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