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The Springbok first five-eighth will head to French Top 14 side Montpellier.
The Bulls, however, will welcome back the experienced Morne Steyn for the 2020 season.
Pollard has long been linked to the Top 14 and will join several other Springboks in the south of France, including Bismark du Plessis, Ruan Pienaar and Frans Steyn.
"Handre has been a true servant to us for six years," Bulls CEO Alfons Meyer said in a media release.
"He will be missed for sure, but we cannot fault his decision to continue his career in France. We wish him well."
Pollard, who is expected to start at first five-eighth for the Springboks at the World Cup in Japan later this year, has played 56 times for the Bulls to go with 39 test caps for South Africa.
He will be replaced in the squad by the experienced Steyn (34) who left the Bulls in 2013 to join Stade Francais in Top 14.
He had made 124 Super Rugby appearances and remains the leading points-scorer for the Pretoria-based side in the competition with 1449.
"It is great for us, he is a very experienced player who can still play at the highest levels," Meyer said.
"He knows the culture and passion of the Bulls as well as anyone and will no doubt contribute massively, not only on the field, but also off it."
Pollard is the latest of a number of Bok internationals set to leave Super Rugby after the World Cup, with South African Rugby admitting they cannot match the salaries on offer in Europe and Japan.
They have relaxed the eligibility rules for Boks playing overseas, but said they will strictly enforce the international window and make sure leading players return from their clubs for tests.