By Francois Murphy

VIENNA (Reuters) -Austria's first three-party coalition since the aftermath of World War Two took office on Monday, ending the country's longest-ever wait for a new government and keeping the Russia-friendly, far-right Freedom Party (FPO) out of power.

Although the FPO won September's parliamentary election with about 29% of the vote, the eurosceptic party failed to form a workable coalition, opening the door to a centrist alternative.

When the FPO bid crumbled, the conservative People's Party (OVP), Social Democrats (SPO) and liberal Neos struck an alliance, overcoming their own earlier failure to do a deal.

The new government takes office after two years of recession, and plans spending cuts and tax hikes on big business to bring Austria's budget deficit back within European Union limits and avoid disciplinary proceedings from Brussels.

New Chancellor Christian Stocker of the OVP must also address widespread unease about immigration and integrating migrants, following a deadly knife attack by a Syrian refugee and planned Islamist attacks that were foiled.

Those concerns have lifted the FPO, whose leader Herbert Kickl has benefited from rising support for the far-right in Europe and called for an end to sanctions against Russia, backing U.S. President Donald Trump's overtures to Moscow.

Had the latest centrist coalition effort failed, there would have been few alternatives to a snap election, which polls suggested would have increased the FPO's share of the vote.

"I wish you in the fulfilment of your duties all the best, much success, and also the necessary bit of luck, and I look forward to working well together," President Alexander Van der Bellen said as he swore in the new cabinet.

The OVP will head the interior and defence ministries while the Social Democrats will control finance and justice, with the liberal Neos running foreign affairs.

Although the three parties have agreed a 200-page government programme, they will have to hammer out many more policies as they go along, potentially causing tensions in their alliance.

"Will it be easy? No. Are the negotiations over? No," Neos leader Beate Meinl-Resinger said on Sunday, pledging "five years of tough negotiation" with the other parties.

The FPO will pressure them throughout.

"The only thing that unites this loser, traffic-light coalition is thirst for power," the FPO said on X on Monday, referring to the three-way coalition in neighbouring Germany that collapsed late last year.

(Reporting by Francois Murphy; Editing by Dave Graham and Alex Richardson)