It is hoped the acquisition, expected to finalise on July 1, will enable MAB to further grow its adviser numbers and market share.
In May the firm reported a 5 per cent increase in adviser numbers from the start of 2019, after numbers grew by 135 throughout 2018.
The advice firm also reported an increase in revenue and productivity over the course of the year, despite Brexit uncertainty and a drop in housing transactions.
The latest acquisition will boost earnings "significantly", according to MAB.
First Mortgage is a Scottish broker with more than 90 mortgage and protection advisers, 15 ‘mortgage shops’ and a telephone advice service.
In 2018, the company arranged £2b in mortgage lending and achieved a profit before tax of £1.5m in the nine months to December 31.
Following the acquisition, MAB plans to develop First Mortgage's omni-channel growth strategy, particularly its telephone service, through the rollout of the Bureau’s own new technology.
MAB is acquiring the shares from Ian Robert McGrail, managing director of First Mortgage, and Robert Lawrence McGrail, director, who own 50 per cent of the business each.
Mr Ian McGrail will retain a 20 per cent shareholding in the firm and remain in his current role of managing director.
MAB stated it would fund the acquisition from a mix of its own cash resources and a partial drawdown on its debt facilities.
Ben Thompson, managing director at MAB, said: "This acquisition is central and complementary to our strategic objective to grow our market share of new mortgage lending.
"First Mortgage is a highly reputable, forward thinking business of significant scale with a clear strategy to deliver further strong year on year growth.
"This enables us to pursue at pace our aim to accelerate group growth through excelling in areas of specialisation, and in particular, building on our omni-channel choice for customers."
Mr Thompson went on to say that the approach best positioned the Bureau to benefit in an evolving intermediary sector and noted the firm’s new technology would further strengthen this ambition.
He added: "I am delighted that Ian has chosen to work with us, to help us both to really accelerate our respective growth plans and am excited at the prospect of making this highly successful and enjoyable for both teams."
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