The company had been chosen by KPMG as preferred bidders last month.
Ferguson, which went into administration with the loss of 70 jobs, will be renamed Ferguson Marine Engineering.
Mr McColl has promised to upgrade facilities at the Port Glasgow yard and seek work in the renewables sector.
He also hopes to grow the workforce from its pre-administration level of 77 to 120 people.
Joint administrator Blair Nimmo said: "It is extremely pleasing to secure the sale of Ferguson Shipbuilders in such a short timeframe and to buyers who can see the potential in the business and its skilled workforce.
"We would like to thank those employees, and all parties with an interest in Ferguson Shipbuilders, including various government agencies, for their patience and support during this period.
"We would also like to wish Clyde Blowers Capital every success for the future.
"As new owners they have an ambitious vision to build on its heritage and grow a successful shipbuilding and marine engineering business on the Clyde."
Mr McColl said: "We are pleased to have completed the purchase of Ferguson's and are excited by its potential to grow into a leading marine engineering business."
He added: "Work is now well underway to develop a plan to rebuild Ferguson's, and we look forward to working with the key stakeholders in that rebuilding process."

Uefa has taken the disciplinary action following some of the Italian club's fans' continued racist behaviour.
Earlier this season, the Rome-based club were fined £120,000 by Uefa following racist chanting in a Europa League game against Tottenham Hotspur.
Lazio supporters have been found guilty of racist behaviour by Uefa four times during the current campaign.
The latest incident came during their Europa League last-32 match against Borussia Monchengladbach on 21 February.
The Serie A club won the second leg 2-0 to progress 5-3 on aggregate.
Uefa said the two-match supporters' ban will start with Lazio's Europa League game against VfB Stuttgart on 14 March.
"The remaining game behind closed doors applies to the next Uefa competition match for which the club would qualify. The Italian club have also been fined 40,000 euros (£34,475)," Uefa added.
Lazio president Claudio Lotito said the sanction was "incredible" and that his club would appeal against the decision.
"To suffer a punishment of one or two games behind closed doors, which will cause serious economic damage to the club and prevent fans from participating in an event like this, seems absurd to me," he added.
Meanwhile Uefa has also warned Turkish side Fenerbahce that they face suspension from European competition if problems with supporters continue.
The club's last European game, against BATE Borisov, was played behind closed doors but was still disrupted when fans threw fireworks from outside the stadium.

Proposals to cut the cultural programme and libraries, as well as increasing parking charges, were ruled out.
However, reductions will be made in sports funding.
Opposition budgets had been put forward by the SNP and Liberal Democrats. Council leader Jenny Laing said protecting frontline services and jobs was the budget priority.
She said: "We have a balanced budget which protects frontlines services, jobs and will also drive inward investment into the city.
"Our approach to the savings has been to focus on back office efficiency savings."
The council has a Labour-led administration.
Administrators have confirmed the sale of Ferguson Shipbuilders in Inverclyde to businessman Jim McColl's firm, Clyde Blowers Capital.
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Lazio have been ordered to play their next two home European games behind closed doors following crowd trouble.
[NEXT_CONCEPT]
Aberdeen City Council has approved its budget for the next financial year, with more than £25m of savings.