The deal also includes a club option for an eighth year and is expected to be made official Sunday, according to reports.
Yelich, 23, emerged as one of Miami's top young players last season, batting .284 with nine home runs and 54 RBIs.
"He's very mature for his age," Marlins manager Mike Redmond told reporters Wednesday morning. "It's amazing when you watch him play and watch his at-bats, and his approach, how professional they are at such a young age.
"He's hungry, and that's what you want. You want young guys to come to the big leagues, and they aren't satisfied with one good year. They want to be better, and that's how you build championship teams, is to have young players that are hungry and want to win, and will do whatever they can to help the ballclub."