Stir will handle trade press for the FTSE 100-listed firm, which makes cans for brands such as Red Bull and PepsiCo. Stir will target trade press including packaging, design, food and drink titles and business press, as well as running the firm's press office function.
The agency will also target events such as trade show Drinktec to position Rexam as a leader and innovator in the sector.
Incumbent agency Madano, which had held the account for a number of years, and one other agency are understood to have pitched for the work.
Rexam comms manager Mark Bunker said: 'We selected Stir to be our PR consultancy because of its in-depth knowledge of the beverage industry and insightful yet creative approach to our brief.'
Rexam switched its financial PR duties from FTI Consulting to Tulchan towards the end of 2012.
At the beginning of this year, Rexam finalised the sale of its under-performing personal care division, which made plastic packaging for brands including L'Oreal.