The 34-year-old England international, who scored 15 league goals last season, has signed a three-year deal.
"It's great to be back," said Defoe, who as a teenager spent the 2000-01 season on loan at Bournemouth from West Ham, scoring in 10 successive matches.
"It was an easy decision, joining a top team with a top manager. The one thing I can guarantee is goals."
The former Tottenham, Portsmouth, West Ham and Charlton player is seventh on the Premier League all-time goals list with 158 in 468 appearances.
Cherries manager Eddie Howe said Defoe's signing is a "huge moment for the club".
Defoe moved to Sunderland in January 2015 after a brief spell at MLS side Toronto and, after saving the club from relegation in the 2015-16 season with 15 goals, signed a contract extension until 2019.
There was a clause in his contract that allowed him to leave on a free transfer if Sunderland were relegated, which he was able to trigger when the Black Cats finished bottom last season.
Defoe made his England debut in 2004 and played at the 2010 World Cup, but did not feature for the national side between 2013 and 2017.
His excellent form last season earned him a recall to Gareth Southgate's side, and he scored his 20th international goal against Lithuania in a World Cup qualifier in March.
Defoe is Bournemouth's second signing of the summer, following the arrival of goalkeeper Asmir Begovic from Chelsea.
"We want to bring players here who can have a big impact on our continued rise and we believe Jermain fits that as a natural, proven goalscorer," added Howe.
The Cherries finished ninth in the Premier League last term - their second season in the top flight.
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Kelso, Galashiels, Peebles, Hawick, Selkirk and Eyemouth saw increases but numbers fell in Duns and Jedburgh.
Figures in Melrose also rose sharply compared with 2014 but exceptionally low levels were recorded that year due to "atrocious weather".
Councillor Stuart Bell said it was "pleasing" to see numbers rising.
A survey has been carried out across the region since 2007.
The latest figures were collected during September and October 2015 with the rise in the region higher than the Scottish average of 2%.
Last year numbers fell by 11% but this was largely blamed on the very low levels recorded in Melrose.
Mr Bell said: "These figures are only ever going to give us a snapshot of a short period of time and can fluctuate depending on weather, however it is pleasing to see that overall average footfall has increased and the figures for several towns are particularly encouraging.
"We need to build on these increases in footfall and the council, partner and community organisations and businesses can all play their part in that, making our town centres as attractive as possible to local shoppers and visitors to the Borders.
"This study started in 2007 and has in effect charted the impact of the recession and increase in internet shopping on our town centres, which largely accounts for the 23% reduction in footfall over that period."
He said the issues were not unique to the Borders and would remain challenges in the longer term.
Sunderland striker Jermain Defoe has re-signed for former club Bournemouth on a free transfer.
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A town centre footfall study in the Borders has recorded a 6% rise across eight main towns in the region in 2015 compared with the previous year.