Advent has offered Brammer 165p per share - representing a 69.2% premium on its 97.5p share price on 22 November.
However, it still marks a discount from Brammer's pre-Brexit value. The company's market value collapsed in the wake of the referendum, with shares falling from 180p on 23 June to just 60p a week later.
Brammer's board has called the offer "fair and reasonable" and is urging shareholders to back the deal.
The company, which is headquartered in Manchester, is set to embark on a turnaround plan under its new owners, after issuing a profit warning in October.
Brammer announced last month that it would not be proposing a dividend and did not expect to report a pre-tax profit for full-year 2016, amid declining sales.
Group sales per working day were down 2% in the third quarter at constant currencies.
Brammer's chief executive Meinie Oldersma said in October that the company needed to focus on its core business, reduce its stock and cut costs.
Commenting on the deal, Advent managing partner Jan Janshen added: "We have admired Brammer's business for some time and are delighted to have the opportunity to partner with Brammer to further strengthen its leading position in the European industrial MRO distribution market.
“Advent's deep sector expertise and our operational focus will help Brammer to execute a turnaround strategy and strengthen its commitment to its customers and suppliers.”
Advent International says it has invested in over 315 private equity transactions in 40 countries and had 40 billion US dollars (about £32.2bn) in assets under management as of 30 June.
Shares were trading higher by 69.5% in mid-day trading.