Tusk said it was good that a leader of his calibre and experience was returning.
"In the months ahead, there is an imperative as never before to deliver at the high political level, both in Europe and further afield. In this respect, Ireland's strong economy recovery and healthy democracy are encouraging," said Tusk, a former Polish Prime Minister.
Kenny was re-elected after 10 weeks of deadlock that followed an inconclusive general election in February.
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Kenny is the first Fine Gael Prime Minister to win re-election in Irish history, though his triumph is marred by a minority administration that is propped up by independent MPs and, more crucially, by Fianna Fáil.
The party, which will remain on the opposition benches, has agreed to support the Fine Gael government for a period of two years in an unprecedented political ceasefire between the rivals.
Kenny's centre-right party lost 26 seats in February's general election but remained the largest party in Parliament with 50 seats. Fianna Fáil made a stunning recovery from a historical low of 21 seats in the 2011 general election to win 44 seats. Sinn Féin remained the third-biggest party with 23 seats.
On Friday Kenny received 59 votes, with 49 against, in the 158-member Parliament - by far the fewest votes ever received for a winning premier in Ireland.
Meanwhile, people across Ireland are being urged to "phone a friend" in Britain and tell them to vote in next month's EU referendum in a move that experts say could tip the balance in favour of 'Remain'.
With polls split 50-50 and the Irish diaspora estimated to include up to five million UK-resident voters, 'Remain' campaigners and the Irish business community believe the 'Irish vote' could be crucial if the outcome in the June 23 vote remains on a knife-edge.
The 'phone-a-friend' social media campaign has been launched by the European Movement Ireland, an independent European advocacy group based in Dublin.
Alastair Campbell, the former Downing Street spin-doctor, endorsed the campaign last month in a speech in Dublin, in which he urged an audience of senior Irish businessmen to make a personal resolution to recruit one UK-Irish voter to the 'Remain' camp every single day.
Elsewhere, European Commission President Jean-Claude Juncker says all Europeans want Britain to remain in EU and that a fair deal on reforms was struck with Britain in February.
A British exit from the EU would have unforeseeable consequences for European cooperation, he said in an interview with German media.
In the interview with the Funke Mediengruppe press group published on Monday, Juncker warned that a so-called Brexit would "surely have unforeseeable consequences on European cooperation, about which I absolutely do not wish to speculate about because I am convinced that Britons will make the reasonable decision."