CGI Group, which has a presence in Ottawa, will also assume $499 million of Logica's debt.
Logica's shareholders had voted 99.5 per cent in favour of CGI's offer at a meeting in July and required regulatory approvals were received.
As a result of the acquisition completion, 46.7 million subscription receipts that were previously issued to Caisse de depot et placement du Quebec will be automatically exchanged into new Class A shares in CGI on Monday.
CGI now has about 72,000 employees in more than 40 countries and $10.4 billion in pro forma annual revenues.
"With the closing of the transaction, our focus is squarely on meeting the expectations of our clients and welcoming our new employees to the CGI family," stated president and CEO Michael Roach.
The company also announced a global reorganizing of its executives, naming presidents for several regional divisions.
Kris Thompson of National Bank Financial increased his target price for CGI shares by $6 to $32.
In a research report, the analyst said he expects Logical will drive a 35 per cent increase in CGI's earnings per share in fiscal 2013, above the 25 to 30 per cent CGI suggested when it announced the transaction.
Over three years, he said the deal will add about $3 per share and CGI will find more than $200 million in planned cost savings that will require additional restructuring costs.
It will also help to push CGI to generate nearly $1 billion of cash flow, enough to continue an aggressive share buyback and satisfy terms of its credit facility.
Despite Europe's economic challenges Thompson said CGI's European footprint opens doors for larger contracts with global customers as the company becomes the world's 11th largest IT services vendor.
Founded in 1976, CGI Group is one of the largest independent IT and business process services firms in the world with about C$4.3 billion in annual revenues.
On the Toronto Stock Exchange, its shares gained one cent at $24.43 in morning trading.