La Liga side Sevilla, who announced the agreement on Saturday, will reportedly pay a club-record €20million initial fee plus add-ons to Samp, who retain a sell-on clause allowing them to profit if the Colombia international moves in the future.
Striker Muriel scored 11 Serie A goals for Samp last season, matching his previous season high achieved with Udinese four years ago, and also contributed a team-leading five assists in his 31 appearances.
Muriel, who joined Samp from Udinese in January 2015, has played in Spain once before in a loan spell with Granada in 2010-11.
He also represented Lecce on loan from Udinese, having previously made his professional breakthrough with Deportivo Cali.
Muriel is Sevilla's third signing of the close-season, following the arrivals of Ever Banega and Guido Pizarro.