Mulder has been working as an analyst with ESPN since 2011.
Mulder's agent Brian Charles confirmed the report, and the agreement also includes an invitation to spring training.
If Mulder makes the team and meets certain incentives and award bonuses, the deal could be worth more than $6 million, according to the report.
"Mark chose the Angels because he has an opportunity to compete for a spot in the starting rotation. Along with the Angels being a championship-caliber club, that made it a good fit,'' Charles said.