The 24-year-old Sporting captain will be out of contract in June and, according to the Primeira Liga outfit, will join Reading next month 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."
Reading confirmed on Monday evening they had struck a deal for the former Portugal Under-21 international to join the Royals on an initial two-and-a-half year contract, with the option of an extra year after that.
A statement on the club's website, www.readingfc.co.uk, read: "Reading football club are delighted to confirm we have agreed a deal to sign Sporting Lisbon's club captain, midfielder Daniel Carrico.
"The 24-year-old joins the Royals to begin the club's investment in this January window.
"He is a versatile player and can play in the centre of defence as well as in midfield. He has signed a contract until the summer of 2015, with the option of a further year."
Reading said Carrico, who has only made two appearances for Sporting this season because of his contractual situation, will join up with his new team-mates later this week.
Reading are second-bottom of the Barclays Premier League and five points adrift of safety. They face Spurs at White Hart Lane on Tuesday and host West Brom this weekend.