The 24-year-old Sporting captain will be out of contract in June and, according to the Primeira Liga outfit, has joined Reading in a 750,000 euros deal which includes a sell-on clause for a future transfer.
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."