The deal sees Stewart McColl's listed company buy Alsop's business from Alsop and a group of venture capitalist shareholders for £1.8 million.
Both parties argue that the deal will match Alsop's 'creative flair' with the SMC Group's 'focused approach to project delivery'.
The deal is by far SMC's most high-profile deal to date. It represents the sixth acquisition by the group since it was floated last summer.
News of the deal first emerged last weekend ( SMC on verge of shock Alsop takeover).
In a statement released late yesterday, both McColl and Alsop said they were delighted with the deal.
McColl said: 'I am very excited at being able to bring into the SMC Group such a world-renowned architect as Will Alsop and his team.
'This acquisition will increase our profile within the international architectural industry, significantly increasing our global exposure, particularly to larger, higher-margin projects.'
Unsurprisingly, Alsop agreed: 'At Alsop's, we attract exciting and dynamic design commissions from all around the world,' he said.
'Joining the SMC Group will allow us to continue to apply our creative skills within a successfully structured business environment, with a strong project-implementation record,' he added.