The group, founded by Lee Cash and Hamish Stoddart 10 years ago, will spend £500k converting the Victorian venue into a pub with a 54-cover dining area, a 24-cover private dining area and open kitchen.
Cash said The Star & Garter, which also becomes Peach's fourth in Warwickshire, was a good fit with the brand.
“Like many who use our pubs locally we have long thought that Leamington was the perfect spot for a Peach pub and, after what turned out to be a long search, we’ve finally found the right pub we can make Peachy," he said.
“The Star & Garter has all the things we look for in a pub – a characterful building in a great residential area that needs some love and attention to make it great again. And that’s just what we’ll be doing.”
The pub, which will create 25 new jobs, will be overseen by Peach managing partner Jez Kynaston when it opens in October.
Kynaston, who has been in charge of Peach's three other pubs in Warwickshire for several years - The Rose & Crown, The One Elm and The Almanack - will focus his time on developing the Star & Garter and The Almanack in Kenilworth going forward.
He said: "Having lived and worked for the past few years in Warwick and talked to people about what they want from a great local, I know we can do it again here in Leamington and create a really great gastropub for everyone to enjoy.
“We want it to be a really smart but welcoming place where our guests will find good food and drink and friendly service, and have a great night out as well.”
Peach has also recruited a new head chef - Tom Lilley - who will oversee the pub's food offering. Lilley will introduce an all-day menu based on Peach's approach of serving seasonal food sourced from ethical suppliers.