For two of the three years Guardiola was at Bayern Munich, Ten Hag was in charge of Die Roten's second team.
Speaking ahead of his side's Premier League meeting with Watford this weekend, the Catalan coach backed the Red Devils' decision to bring in the Ajax manager.
"Watch his Ajax team and you see his qualities," Guardiola said. "Congratulations to Erik and wish him all the best. He is a top class manager, his teams are a joy to watch at a team like Ajax."
Guardiola and Ten Hag have never squared off as managers previously, but they are set to meet in at least two Manchester derbies next year.
Unlike United, City are still competing on multiple fronts this season. They currently sit top of the Premier League by one point and face off against Real Madrid in the Champions League semi-finals over the next fortnight.
They will not be appearing in the FA Cup final though after falling to defeat against Liverpool in the semi-finals earlier this month.
For more from Matt O’Connor-Simpson, follow him on Twitter