The management team bought Inverurie-based Arnlea from Aberdeen businessman Mark Cavanagh, who said he was "very satisfied" with the deal.
The management buyout reflects strong investor interest in oil services businesses.
Arnlea has developed software that oil and gas firms can use to automote the procedures they follow to keep tabs on costly assets and to complete associated regulatory reports.
Led by Allan Merritt, the company's client base includes giants like BP and Total.
Noting the firm has made good progress in overseas market Mauro Biagioni, director at NVM, said the company had "massive market potential".
The deal also includes the NexusAB risk management operation.
It is the latest in a series in which private equity firms have bought into Scots engineering businesses that they believe could capitalise on booming activity in global oil and gas markets.
In December, Glasgow-based Maven Capital Partners bought a controlling stake in the R&M Engineering oil services business from Robbie Mackay in a £5m deal that showed its faith in the North Sea market.
Mr Biagioni said: "We are delighted to back an experienced and high quality management team from two businesses that have the potential to create a large international company."
He said NVM had provided around £1m development capital to support the team's growth plans.
Mr Cavanagh bought Arnlea in 2012 from oil and gas entrepreneur Ian Suttie's First Tech investment vehicle. He acquired NexusAB in 2011.
The prices of those deals were not disclosed.
Asked why he sold the firms to the MBO team, Mr Cavanagh said: "I am just an investor. I purchased the businesses built them up and sold them on."
Mr Cavanagh runs the XPD8 oil and gas engineering business.
Mr Merritt joined Arnlea last year. He was previously chairman of Abermed, an oil and gas occupational heath firm that NVM backed.
NVM sold Weldex to Dunedin Capital Partners in 2010 in a deal that valued the crawler crane firm at £100m.