The contract, which will begin on 1 April, covers Tate Modern on Bankside and Tate Britain at Millbank.
Works will include care and management of lawns, trees, hedges and borders, irrigation management, tree, shrub and herbaceous planting as well as maintenance of hard landscaped surfaces.
The landscape at Tate Modern - formerly Bankside Power Station - was designed by the Kienast Vogt Partnership in association with Charles Funke Associates.
The area was planted with 800 2m high yews and 1,000 5m semi-mature birch when it was developed.
The contract is valued at between £120,000 and £160,000 and may be extended by two years.
The deadline is 4 January. Contact Dennis Ahern, Tate, Millbank, London SW1P 4RG or email firstname.lastname@example.org.