Carteron guided Zamalek SC to the Egyptian Super Cup and CAF Super Cup titles earlier this year during a nine-month spell in charge and resigned from the post this week.
The 50-year-old won the CAF Champions League crown in 2015 with Congolese side TP Mazembe and also has prior experience in Saudi soccer with a stint at Al Nassr in 2017.
He will arrive shortly in Doha where Al Taawoun are playing in the AFC Champions League.
The club are top of Group C in Asia's elite club competition with six points from three games, level with Qatar Stars League champions Al Duhail, and take on Iran's Persepolis on Friday.
Campelos left his role with Al Taawoun in August. Abdullah Aseeri took over on an interim basis and helped the club avoid relegation on the final day of the campaign. (Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Peter Rutherford )