The company – which employs several hundred staff in Scotland – has agreed a deal with I Squared Capital and TDR Capital following talks. The private equity firms agreed the offer worth 880p per share, representing a 39 per cent premium on Aggreko's share price on February 4.
Chairman Ken Hanna said the board believes the offer "represents an attractive price in cash that fairly recognises Aggreko's future prospects".
He added: "Aggreko is a great company and the actions that we have taken in the last few years, both strategically and financially, have positioned the company well to navigate the market challenges and look to the future as a leader in the energy transition.
"I am proud to have been chair of Aggreko for the last nine years and it has been a pleasure to work with so many dedicated individuals who have made Aggreko a leader in the field of temporary power solutions.
"For now, it is business as usual, and I thank all our people for their continued dedication and hard work."
The company, which supplies temporary power generators, has seen trading severely affected by the coronavirus pandemic.
On Monday, it reported that pre-tax profits were cut by almost half in 2020 to £103 million.
The takeover will be need at least 75 per cent approval from shareholders at its forthcoming general meeting and is expected to complete in the summer if it receives the go-ahead.
Adil Rahmathulla of I Squared Capital, said: "Aggreko is a global market leader in delivering bespoke temporary power solutions to its customers and has clearly shown it has a strategy to complete its journey towards a net-zero emission business.
"We are well-positioned to accelerate Aggreko's development at this critical juncture and secure a successful future for the company, underpinned by a long-term investment focus and the combined expertise of TDR Capital and I Squared Capital in the power infrastructure and equipment rental sectors."
Aggreko announced in January that it was investing £4.5m to upgrade its production facility in a move uniting its three Dumbarton operations, “creating a future-energy hub that will play a key role in our transition to a low-carbon operation”.
It also confirmed that it had sealed a major contract for this summer’s rejigged Tokyo Olympics – and it said this week that its global events team was “progressing well” with its preparations for the event.
The firm was founded in the Netherlands in 1962, with its moniker created by combining the Dutch word for generator – “aggregaten” – and the name of founder Luc Koopmans.
It relocated its headquarters to Scotland in the 1970s, and has helped deliver power for Pink Floyd touring the US in the 1980s and the Grateful Dead in the 1990s – listing on the stock exchange in 1997.
Other events utilising the company’s kit include Glastonbury and the Super Bowl – and it provided power for the Glasgow 2014 Commonwealth Games.