UPDATE 2-Australia's Uniti agrees to $2.7 bln takeover offer from Brookfield, Morrison & Co

(Adds shares, deal details and background)

April 14 (Reuters) - Uniti Group has agreed to a nearly A$3.62 billion ($2.70 billion) takeover offer by a unit of Canada's Brookfield Asset Management Inc and fund manager Morrison & Co, the Australian telecom firm said on Thursday.

Uniti shares, which have surged more than 50% since entering exclusive talks with Morrison on March 15, were up 3.1% at a record high of A$4.97 in early trading.

Under the potential deal, Uniti shareholders will receive A$5.0 per share, representing a premium of 58.7% to the stock's closing price on March 14, a day before the telecom firm received an initial A$4.50 per share offer from Morrison.

Uniti's board unanimously recommended that its shareholders vote in favour of the proposal.

Late March, the Morrison-Brookfield consortium matched a rival offer of A$5 a piece from Macquarie Group's asset management arm and Canada's Public Sector Pension Investment Board for Uniti.

The proposal required the Australian telecom firm to not engage further with the Macquarie-led consortium or grant it due diligence access.

The proposal for Uniti is Morrison & Co's latest venture into the telecom space after funds managed by it acquired a 49% stake in Telstra's mobile tower business last year.

Brookfield has also been involved in a number of deals in Australia. In recent weeks, its investment vehicle bought asset manager La Trobe Financial in a $1.1 billion deal, and it had also tried to buy power producer AGL Energy.

($1 = 1.3428 Australian dollars) (Reporting by Harish Sridharan in Bengaluru; Editing by Vinay Dwivedi and Sherry Jacob-Phillips)