Emery had a year left to run on his existing contract at the Europa League champions, but has decided to call time on his spell in southern Spain.
The 44-year-old has been linked with several clubs in Europe, including French champions Paris Saint-Germain and Premier League Everton.
Sampaoli, who has never coached in Europe, will hold discussions with Sevilla officials over the vacant managerial position on Monday.
"Emery's intention is to, throughout this week, resolve unilaterally his contract with Sevilla because of his wish not to continue as coach of the first team for the 2016-17 campaign," Sevilla confirmed in a club statement.
"Following the Basque coach's irrevocable decision to terminate his contract with Sevilla, the club has moved to find his successor.
"Former Chile coach Jorge Sampaoli will arrive in Seville on Monday to begin talks with the club."
According to Spanish newspaper Marca, Emery will compensate Sevilla by paying €2m (£1.6m) to be released from his current contract.
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