Mansourian has been without a team since parting company with Zob Ahan in December 2019.
The 48-year-old coached Iran U-23 football team from 2011 to 2014.
Mansourian will replace Sirous Pourmousavi in the team.
Iran will participate at the 2020 AFC U-19 Championship in Uzbekistan in October.
The top four teams of the tournament will qualify for the 2021 FIFA U-20 World Cup in Indonesia.