The France international will spend the remainder of the 2021-22 campaign on loan at Estadio Ramon, with the move being confirmed on Tuesday.
As it stands, Martial is due to return to Old Trafford this summer, where he could be in the plans of the new manager.
However, the 26-year-old has suggested that he would be open to completing a permanent move to the La Liga outfit depending on how the rest of the season unfolds.
"I have joined for five months but you never know what the future holds. It's not just about money. It's to play and to enjoy it. That's it. That's why I chose to come here, to play and to enjoy football again," Martial told reporters.
"I want to play more and show what I can do. I believe Sevilla is the perfect place to do that. I want to score goals, provide assists and be crucial for this team in the next five months. There are many good players at Sevilla and I want to bring my experience to the side.
"It [negotiation] hasn't been easy. But from the first day, I knew I wanted to come to Sevilla and we all worked for that to happen.
"The coach [Julen Lopetegui] and the sporting director [Monchi] showed a strong interest in me and that's what convinced me to come here. They [Sevilla] wanted me in the past and we kept in touch. They contacted me recently and said I could help them.