Senegal's army spokesman told Reuters, Censor.NET reports.
Barrow took the oath of office as Gambia's president on Thursday at its embassy in neighboring Senegal, calling for international support from West Africa's ECOWAS bloc, the African Union and the United Nations.
"We have entered Gambia," Senegal's army spokesman Colonel Abdou Ndiaye told Reuters.
Nigeria, which pre-positioned war planes and helicopters in Dakar, said in a statement that it had also deployed military assets "to protect the people of the Gambia and maintain sub-regional peace and security." It was not immediately clear, however, if they too had crossed the border.
Ghana has also pledged troops.
"This is a day no Gambian will ever forget," Barrow said after taking the oath, which was administered by the president of Gambia's bar association. "Our national flag will now fly high among the most democratic nations of the world."
"I hereby make an explicit appeal to ECOWAS, the (African Union) and the U.N.... to support the government and people of Gambia in enforcing their will, restoring their sovereignty and constitutional legitimacy," he said.
The U.N. Security Council on Thursday backed ECOWAS's efforts to ensure Barrow assumes power, and the United States said it supported Senegal's intervention.
Ecowas has been attempting to persuade Jammeh to quit for weeks, and has failed to do so, despite his increasing political isolation and last ditch efforts to reason with him overnight.
Jammeh, in power since a 1994 coup and whose mandate ended overnight, initially conceded defeat to Barrow following a Dec. 1 election before back-tracking, saying the vote was flawed.
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