The first summit with Arab leaders will be in Egypt. The second is scheduled in Jordan with King Abdullah.
Conditions permitting, Bush will meet the Israeli and Palestinian prime ministers, a White House spokesman said on Wednesday.
Bush leaves on Friday for a tour of Poland, Russia, and a summit of major industrialised (G8) nations in France.
He will also travel to Qatar to visit US troops who took part in the invasion of Iraq.
The president will visit Egypt, Jordan and Qatar for three days from 2 June. He will add visits to these countries to previously announced stops in Poland, Russia and France from the G8 meeting in Evian.
Bush will travel to Sharm el-Sheikh, Egypt, for the 3 June meetings with Arab leaders.
From Egypt he will travel to Jordan on 4 June for a meeting with King Abdullah of Jordan.
Conditions permitting, he will meet Palestinian Prime Minister Mahmoud Abbas and Israeli Prime Minister Ariel Sharon.
If the meeting with the Palestinian prime minister takes place it will be Bush's first face-to-face meeting with Mahmoud Abbas.