Flight SU100 departed Moscow's Sheremetyevo International Airport on Sunday morning.
The Russian Foreign Ministry said earlier this week that Antonov would spend the next workweek in Washington.
The diplomat noted he is optimistic about Russia-US relations and expressed hope for constructive work in rebuilding bilateral ties.
"I am heading [to the US] with an optimistic mood based on the results of the meeting of two presidents [Vladmir Putin and Joe Biden]. I look forward to constructive work with American colleagues to build equitable, pragmatic relations. Tomorrow and in the days to come, there are plans, scheduled meetings and lots of work. We are counting on progress", he said.
Antonov and US Ambassador to Russia John Sullivan travelled to their home countries for consultations this spring, as ties between the two nations deteriorated.
However, at their summit in Geneva earlier this week, Putin and Biden reached an agreement on the ambassadors' return. Sullivan also confirmed on Saturday that he would return to Moscow soon.