The combined company has approximately 72,000 staff in more than 40 countries and annual revenue of more than £6 billion.
“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,” said Michael Roach, president of CGI.
Tim Gregory has been appointed UK president. Logica was bought for an estimated £1.7 billion.
Last year Logica axed around 1,300 jobs as part of an accelerated restructuring plan.