* Prysmian to pay $290/shr in cash for each Encore share

* Sees run-rate annual synergies on EBITDA of 140 mln euros

* Deal approved by both boards

* Transaction expected to be finalized in H2

April 15 (Reuters) - Italy's Prysmian announced a deal to buy U.S. firm Encore Wire for an enterprise value of about 3.9 billion euros ($4.15 billion) as it doubles down on a North American market that already powers its profits.

Massimo Battaini, CEO-designate of the world's largest cablemaker, described wire and cable maker Encore as a "strong player" in the U.S., in particular in the industrial construction segment.

It will pay Encore Wire shares $290 in cash each, an 11% premium to the stock's close on Friday.

Battaini said the deal would allow Prysmian to become "even more relevant" in the North American market, its most profitable one, thanks to the complementary portfolios of the two firms.

"This ... makes this acquisition highly synergistic," said Battaini, who will inherit the CEO role from Valerio Battista at the group's shareholders meeting on Thursday.

Prysmian shares, which are trading at record highs, rose as much as 7.2% on Monday, giving it a market capitalisation of around 14 billion euros.

The inclusion of Encore will see North America account for more than 30% of Prysmian's core earnings (EBITDA), Battaini said.

It will also mean it reaches its business plan target for an adjusted EBITDA of around 2 billion euros "much faster than in 2027," he added.

The company said it expects the acquisition to generate annual 'run rate' synergies on its EBITDA of around 140 million euros, from commercial activities and cost cutting, within four years from closing of the deal, which is expected in the second half of 2024. This will help Prysmian increase its earnings per share (EPS) by about 30%, it said.

Prysmian said last year it was focused on organic growth with scope for only "bolt-on" acquisitions in specific market segments or geographies using a war chest of around 1.1 billion euros.

"Organic growth remains our major opportunity to capitalize on the growth in drivers and secular trends ... that we see for the market. But you recognize that M&A is in our DNA," Battaini said.

Prysmian, which was created in 2005 after a spin-off from the Pirelli group, has since made two large acquisitions, Netherlands-based Draka in 2011 and U.S.-based General Cable in 2018.

The group will finance the Encore transaction through a mix of 1.1 billion euros in cash and newly committed debt facilities of 3.4 billion euros, the company said.

($1 = 0.9394 euros) (Reporting by Angela Christy in Bengaluru and Giulio Piovaccari in Milan; editing by Savio D'Souza and Jason Neely )