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The 25-year-old midfielder, who signed for the Hammers in the summer of 2023, made 18 appearances for the club, including seven in the Premier League this season.
A West Ham statement said: "Everyone would like to thank Andy for his hard work, commitment and professionalism, and wish him and his family all the best for the future."
Irving made his debut for Scotland over the summer and has admitted to fulfil his World Cup ambitions he needs to be playing regular first team football.
The Scot's contract with Sparta is yet to be disclosed.