Blinken, travelling in West Africa, spoke by telephone with Tshisekedi to congratulate him on his victory, the State Department said.
Blinken "encouraged President Tshisekedi to address the concerns raised by election observation missions by taking steps to promote confidence in the democratic process going forward," State Department spokesman Matthew Miller said.
Tshisekedi officially triumphed with 73.47 percent and the vote passed largely peacefully in a country long torn by violence and instability.
But voting was officially extended by a day due to logistical snarls and polls were open for days afterward in remote areas.
Losing candidates voiced anger at the vote, which the archbishop of Kinshasa denounced as a "gigantic, organized mess."
Blinken also spoke to Tshisekedi about the troubled east of DR Congo amid cautious hopes to bring stability after years of unrest.
The US intelligence chief, Avril Haines, late last year said she had reached agreements on de-escalation from Tshisekedi and President Paul Kagame of Rwanda, accused by Kinshasa of backing ethnic Tutsi rebels that have rampaged in the eastern DRC.
Blinken met with Kagame last week at the World Economic Forum in Davos and praised recent efforts by Rwanda, which has faced US criticism in the past for its role.