Vieira joined Leeds back in 2015 are undergoing a successful trial with the club's academy and went on to make 63 Championship appearances for the club after making his debut aged 17.
The Bissau-born midfielder has signed a five-year contract running until the summer of 2023 with 'Samp'.
The Italian side are believed to have paid an initial £5.8m for the 20-year-old, with a further £400,000 in add-ons.
Vieira's departure has frustrated Leeds fans, who had high hopes for the England U21 international.
The youngster could be involved when Sampdoria get their Serie A campaign underway against Fiorentina on August 19.
August 1, 2018