By Dave Graham and Philip Blenkinsop

BERN/BRUSSELS (Reuters) - Switzerland and the European Union said on Friday they had reached a deal to strengthen their trade ties, overcoming Swiss concerns about immigration and opening the door for the biggest overhaul of bilateral relations in years.

The joint negotiations began in March and delved into contentious areas of sovereignty such as how to resolve disputes where Swiss and EU law diverge in a bilateral trade relationship worth some 300 billion Swiss francs ($338 billion) annually.

Though it faces big tests before ratification, the accord is a step forward from the last bid, which failed in 2021 when Bern abruptly pulled out. It also delivers a boost to the EU as it tries to move past Britain's 2016 vote to exit the bloc.

Swiss President Viola Amherd and the president of the European Commission, Ursula von der Leyen, announced the political agreement at a joint news conference in Bern.

"Today is a milestone for the stabilization and further development of bilateral relations," said Amherd, the head of Switzerland's seven-member executive, the Federal Council.

Von der Leyen described the agreement, which could see Swiss financial contributions to the bloc rise in a few years, as "historic" and vital given geopolitical tensions.

"In Switzerland as well as in our 27 member states, in this challenging environment, strong partnerships like ours are not just an advantage, they are a must," she said.

The deal covers areas ranging from electricity to state aid, transport and freedom of movement, setting the scene for a tough approval process in Switzerland, which per capita is wealthier than most of the bloc's member states.

Under the deal, Switzerland's annual contribution towards the EU will stay at 130 million Swiss francs ($145 million) in a transitional phase to the end of 2029. From 2030 it will rise to 350 million francs through 2036, the Swiss government said.

Switzerland's economic ties with what is now the EU were built on a 1972 free trade deal subsequently expanded by multiple agreements. However, those accords have begun to age, with some expiring as Europe updates its own regulations.

OPPOSITION TO CLOSER TIES

At the heart of the negotiations has been agreeing on so-called "dynamic alignment" of laws, under which Switzerland is obliged, pending its own constitutional safeguards, to adapt its legislation to relevant ongoing changes in EU law.

Switzerland secured a mechanism with the EU that could let it control immigration from the bloc under exceptional circumstances, subject to a process of joint arbitration.

The Swiss government faces opposition to closer ties with the bloc, fed by concerns on the right over surging population growth and on the left about the erosion of wage protections.

The new deal must still be approved by the Swiss and European parliaments and is almost certain to face a public referendum in Switzerland, where powerful critics are marshalling their forces to reject it.

European Trade Commissioner Maros Sefcovic said the agreement will bring benefits to Switzerland on research, health and air freight, and that it could take effect in 2028/29.

If the agreement is not approved, relations between the two sides would likely suffer, he said.

"Our cooperation would over the time be smaller, would degrade, would be more difficult," said Sefcovic.

($1 = 0.8940 Swiss francs)

(Reporting by Dave Graham, Philip Blenkinsop and Bart Meijer; Editing by Peter Graff and Frances Kerry)