Rosenne was born in Jassy, Romania. He immigrated to Mandatory Palestine in 1944. During the 1950s he studied law at the Sorbonne. He obtained his Ph.D. in 1957. From 1971 until 1979 he served as legal adviser to the Israeli Ministry of Foreign Affairs and took part in the negotiations for the Israeli-Egyptian peace treaty. From 1979 until 1983 he served as the Israeli ambassador to France. From 1983 until 1987 he served as the Israeli ambassador to the United States. In 1987 Rosenne retired from the diplomatic service. From 1989 until 1994 he served as president of the Israel Bonds Organization.
Rosenne was a senior partner at the Balter, Guth, Aloni Law firm in Israel and was active with various Zionist organizations. He was known for supporting Israeli policies regarding the Palestinian-Israeli conflict in his writings and activities worldwide.
Rosenne died on 14 April 2015, aged 84. In memoriam, Colette Avital writes: "Until the end of his life, he remained a staunch defender of Israel, granting TV and radio interviews during which he often quoted relevant clauses in agreements signed by the State of Israel or in international conventions by which it was bound".
- "Meir Rosenne(1931–2015)". Israel Journal of Foreign Affairs, IX(2). 2015.