The Royals will pay just over £600,000 (€750,000) to secure the January arrival of the centre-back, whose contract was due to expire in the summer.
Carrico moves to England on a two-year deal, with the option of a further year which would commit him until 2015. He will join up with his new team-mates for his first training session later this week.
Sporting will also receive an unnamed percentage of any sell-on fee for the player, who has been with the club since the age of 12.
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"I leave because I understand that I am at a stage in my career in which I have to take chances. Moreover, the proposed project is extremely exciting one to me and I know I can succeed.
"I wish the Sporting Clube de Portugal to return to winning ways quickly and I ask you also, as captain, to continue to support the team, the club and its officers and employees.
"To all of you who supported me over the years, thank you very much, I'll take you with me in my heart."
Carrico will become the first arrival of what boss Brian McDermott expects to be a busy January for Reading.
"I think we're going to do some stuff," he told reporters on Monday. "We'll see what it is but I think we'll definitely be doing something."