It was announced last week that the Yorkshireman would go under the knife but his period of absence was unknown.
The England and Wales Cricket Board on Thursday said Bresnan will undergo a six to eight week period of rehabilitation, meaning he could be back for the first Test against New Zealand which starts on May 16.
The ECB statement read: "England and Yorkshire bowler Tim Bresnan has undergone an uncomplicated operation on his right elbow to remove extra bone and scar tissue.
"Bresnan will now commence a six-eight week rehabilitation and back to bowling programme before returning to competitive cricket early in the summer."
Bresnan has been troubled by his right elbow for some time and had a first operation on the joint late in 2011.
He struggled for form in 2012, finishing the year with two wicketless Tests in India following a lean series against South Africa.
The injury ruled him out of the ongoing tour of New Zealand but he will hope to be ready to face the Black Caps on home soil.
Should he require more time, the ICC Champions Trophy gets under way on June 6.
- Sports & Recreation
- Tim Bresnan