"We look forward to working with president Sleiman in pursuit of our common values of freedom and independence."
Suleiman's election in Lebanon's 127-member parliament was observed by leaders from Qatar, Iran, Syria, France and the EU.
His appointment comes as part of a political deal brokered in Doha on Wednesday by Sheikh Hamad bin Khalifa Al Thani, the emir of Qatar.
Bush said he was "hopeful that the Doha agreement, which paved the way for this election, will usher in an era of political reconciliation to the benefit of all Lebanese."
"The new president fully understands that the presidency should remain above the political differences: He is the arbitrator and not the ruler"
Talal Salman, editor-in-chief of Lebanon's As-Safir newspaper
King Abdullah II of Jordan said the vote was a "positive step for the people of Lebanon and for national unity," according to a statement from the royal palace.
"Jordan stands alongside the Lebanese in their desire and their efforts to preserve their independence and their stability," he said.
David Miliband, Britian’s foreign minister, said Sleiman’s election marked "an important step forward for Lebanon".
"We will continue to support Lebanon's stability, integrity and independence, and we look forward to president Sleiman working with a unity government to bring Lebanon out of its current fragility," he said in a statement.
Horst Koehler, Germany’s president, said he welcomed Sleiman's appointment.
"I wish you lots of success, the necessary strength and good luck for the big challenges that lie ahead of you," he said.
Nicolas Sarkozy, the French president, said: "During this period that opens today and facing ... challenges, Lebanon can count now more than ever on the full support of France."
Morocco's King Mohammed VI said Lebanese national unity would be boosted under Sleiman’s rule.
"Thanks to your wisdom, your skills and human qualities, you are going to achieve the aspirations of the brotherly people of Lebanon in strengthening national unity," he said.
Editorials by Lebanese newspapers also discussed Sleiman's accession to the presidency.
Talal Salman, editor-in-chief of Lebanon's As-Safir newspaper, said Sleiman's inauguration speech was measured and neutral.
|Sleiman's election comes after Lebanon's|
leaders reached a political deal in Qatar [AFP]
"He spoke simply and avoided grandiose language. There were no pretensions or unrealistic promises in his speech. He acknowledged all sides without siding with any," he said.
"The new president fully understands that the presidency should remain above the political differences: He is the arbitrator and not the ruler. He has to be the common dominator among all conflicting groups."
Ghassan Sherbel, editor-in-chief of Al Hayat newspaper, said the Lebanese people will expect Sleiman to help restore the Lebanese republic.
"[Sleiman] will have to restore the authority of the presidency, the rights of the state and the dignity of the constitution," he wrote in an editorial.
He said that Sleiman had to help build "a republic that can accommodate all parties and guarantee no more fallen martyrs of internal fighting … where no party feels marginalized, threatened or weakened."