Thursday's deal will pave the way for a formal agreement between the Labour Party of Peres and Sharon's own right-wing Likud party to enforce next year's planned Israeli pullout from the occupied Gaza Strip.
"Peres will be named as number two to the prime minister and will be considered the most important member of the cabinet after the head of government," the statement said.
Five cabinet porfolios have been earmarked for Labour in the new coalition line-up while the key defence, foreign and finance ministries will remain under Likud control.
Sharon, who has been without a parliamentary majority for six months, won approval earlier this month from Likud's central committee to bring centre-left Labour and its 23 MPs into a new broad-based coalition.
Peres has previously served as Israel's prime minister and foreign minister.