The 24-year-old Carrico, who joined from Sporting Lisbon, can play in either defence or midfield and is hopeful of making his Reading bow against the Baggies.
"I hope I can pull on the Reading shirt in the next game," he told ReadingFC Player. "Like I said before it will be a dream come true. I'll be training hard in the week to prepare for the next game and I hope I can play."
Carrico had captained Sporting Lisbon but his appearances were limited this season due to ongoing contract wrangling and he is looking forward to playing in the Premier League.
"I'm really proud to be here," he said. "To play for a team in the Premier League is a dream come true. I'm very happy and glad to be here, and I hope I can help my teammates to go up the table.
"I'm from Lisbon and I have only played for Sporting so far in my career. I've played in the Europa League and Champions League - but now I'm here to help the team and the club and that's what I want to do."
Carrico has now been training at Reading's Hogwood training ground for the past week after penning an initial two-and-a-half year deal with the Berkshire club and the former Portugal Under-21 international is enjoying life under new manager Brian McDermott.
"We have spoken a bit - he (McDermott) has told me what he expects of me on the pitch. I will work really hard in training and show my qualities and what I can do.
"I like the atmosphere inside the group and in the dressing room - they are really good guys and they've helped me a lot coming to a new club."
"I am proud to be the first player from Portugal to play for Reading - so I will have to show the Portuguese quality."