The Hollywood stars will be joined by Sir Elton John, James Taylor, Rosanne Cash and Jennifer Hudson at the annual event on 2 April (12) at New York's Carnegie Hall.
Streep has previously proved her musical talents by singing in her movies A Prairie Home Companion and Mamma Mia! but fans have yet to hear if Tatum can carry a tune.
Tickets for the fundraising concert, which has been given the theme Songs from the Silver Screen, range from $150 (£94) to $600 (£375).
Sting founded the charitable organisation with his producer/actress wife Trudie Styler in 1989 after witnessing the destruction of the Amazon rainforests.