He has been a regular enforcer for South Africa's leading Super Rugby franchise since his 2011 debut, making 39 appearances.
The aggressive second-row had started the opening five matches for The Sharks this season before he injured his shoulder against the Bulls in March.
He is expected to return to Super Rugby this weekend in time to support the club's push for a home playoff.
Bresler, who moves to the capital with wife, Kelly, said: "When I first heard there was interest from Edinburgh Rugby and Alan Solomons [head coach] I immediately did some research to build up my knowledge of the country and the club.
"I read about some big wins and some narrow losses against some of the top teams in the competitions and it struck me as a chance to join a club that's moving in the right direction and where hopefully, together, we'll be able to push on and do some great things.
"I'm really excited. I've always wanted to compete with the best, and this is a fantastic opportunity to take on the top players of the northern hemisphere.
"I'm really looking forward to it."
Bresler's recruitment completes the club's second-row stable, with the Namibian competing with recent Scotland captain Grant Gilchrist; Scotland A capped Fraser McKenzie and Ollie Atkins; and promising twin brothers Alex and Ben Toolis, for a place in the boiler-house.
Edinburgh Rugby head coach, Alan Solomons, added: "Anton [Bresler] is a player who, despite being just 26, has been a regular in The Sharks starting lineup for the past three to four years.
"The Sharks are probably South Africa's strongest franchise and are currently second in Super Rugby, which allows us to appreciate the quality of Anton as a player.
"He is a big, powerful and abrasive player. He's a front of the lineout jumper and I would describe him as more of an enforcer lock."
Anton Bresler (26), second-row
Born: 16 February 1988 in Windhoek, Namibia
Height: 6'6"; weight 17st 11lb
Honours: Natal U18 Academy, Sharks U19, Sharks U21
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