The Edinburgh-based agency won the business after a pitch process, which took place last week.
It will now be responsible for handling an integrated advertising campaign, which is set to roll out nationwide in October. The campaign is thought to include a TV spot.
Baxters, which produces a range of products including gourmet soups, pasta sauces, chutneys and mayonnaise, previously worked with JWT London on its advertising business.
The agency was appointed to the account in August 2009, after a pitch against DHM, The Red Brick Road and Rainey Kelly Campbell Roalfe/Y&R.
Leith's appointment follows the arrival of Yvonne Adam as Baxters' new marketing director.