"In Lucas Torreira, we have signed a young player who is a very bright talent in the game," coach Unai Emery told the club's website.
"A midfielder with great quality, I have enjoyed watching his performances for Sampdoria in the past two seasons, and we all saw him do very well for Uruguay in the World Cup.
"He is a young player already with good experience, but who wants to keep on growing. We welcome Lucas to Arsenal and look forward to him joining us soon for pre-season."
The 22-year-old played all five of Uruguay's World Cup matches in Russia, as they crashed out in the quarter-finals following a 2-0 defeat by France.
Torreira, who made 71 appearances since joining Sampdoria in 2015, expressed his delight at joining Arsenal.
"I feel very happy. I want to make the most of this opportunity life has given me. I am really looking forward to starting this new adventure," he said.
"I feel calm. I am used to coping with this kind of thing in the best possible way. It's a very positive thing that people want to welcome me.
"It makes me feel comfortable. Now I am calm and I look forward to the future, which for sure will be very nice".
Arsenal did not provide financial details of the deal but it was reported last month that the fee agreed would be around 30 million euros. (26.55 million pounds)
Torreira will wear the number 11 shirt vacated by midfielder Mesut Ozil, who has switched to number 10.
($1 = 0.8539 euros)
(Reporting By Arnab Paul in Bengaluru; Editing by Christian Radnedge)
