Barry Ferdinand and Jason Collins signed the deal to regain the London-based investors’ 31% shareholding for £16m, double the £8m that was paid for the original share sale in March 2010.
The agreement upgrades the directors’ stake in the company to 45% each, from around a third each previously.
Nigel Wray, a well-known UK investor, was brought on board to help with funding the buyout, and in turn now has a 10% stake in Apogee.
He was introduced to Ferdinand and Collins through Apogee's chairman Roger Goodman, who is on the board of international recruitment consultancy Networkers with Wray.
Goodman set up the meeting with Wray after "infighting" amongst LMS’ board members led the company to propose the sale of its shares in Apogee to another private equity firm, according to Ferdinand.
Ferdinand said Wray’s track record in investment makes him a "who’s who of how to make money".
"Getting someone like that to invest in our business underpins the success we have had over the past 20 years and what the industry can bring for us. These guys don't put their name to something they feel hasn't got a high chance of succeeding."
He added that Wray will not have any day-to-day input into the running of Apogee, but will act as a "figurehead" for investment decisions and "open doors" for the business through his contacts.
Wray commented: "I am very impressed with both Apogee’s track record and modus operandi. It’s an exciting time to get involved long-term with Jason and Barry at this stage of the company’s future prospects."
Ferdinand and Collins were approached by a number of private equity investors around the time of the LMS deal in March 2010, Ferdinand said, as the directors looked to gain some financial interest to fund what has proved to be an ambitious acquisition programme.
Ferdinand said that the decision to sell shares helped this strategy of having a "smaller bit of a bigger pie" and was insistent that the end of the relationship with LMS does not signal the end of its acquisition strategy, and Apogee now has a facility in place with Barclays to fund further purchases.
In 20 years of trading, Apogee has made 17 acquisitions, with the aim of hitting £150m turnover by 2015.
Ferdinand said: "I think that is very achievable now because there are a couple of large players in the industry which I am sure would be looking to consolidate their positions and we have got an appetite to grow our business."
He added that Apogee was in negotiations with at least two "significant" companies about upcoming acquisition plans.
Apogee’s financial results, which have just been signed off by auditors, Ferdinand said, report revenues of £66m for 2012 with an EBITDA of £10m.
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