The 24-year-old Portuguese has agreed an initial contract to 2015, according to Reading's website, with the option of a further year.
Carrico, a former Portugal Under-21 international, is a defender who has also operated as a defensive midfielder.
Carrico wrote a farewell letter on Sporting's website.
In it, he said: "It is with mixed emotions that I write this farewell message. I'm leaving the club of my heart, where I had the privilege of graduating (through the youth ranks) and serving for several years.
"I'm leaving because I understand that I am at a stage in my career when I have to take chances. Moreover, the proposed project is extremely exciting to me and know I can succeed."
Reading are second from bottom in the Premier League, five points from safety.
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