Barrow's inauguration coincided with the 52nd Independence Anniversary of the West African Country.
"Gambia has changed forever".
USA and British diplomats were finding it hard to enter the stadium, an AFP correspondent reported, as people who had not been able to get inside massed against a heavy security presence.
An accomplished property developer, Barrow had never held public office before winning the presidential election.
However, Jammeh conceded defeat but later took a U-turn on his decision, claiming that the electoral process was tainted with "unacceptable irregularities". Mr Barrow is only the third President in the history of the Gambia.
Jammeh has since fled to Equatorial Guinea.
Mr Jammeh was voted out in December but he only agreed to step aside when regional powers sent in troops ready to remove him by force.
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He has promised to reverse many of Jammeh's policies which stretched over more than two decades of power.
Sall arrived in the country on Friday.
Barrow was sworn-in by the new Chief Justice, Justice Hassan Jallow.
Mr Sall said Gambia and Senegal must strengthen economic and other relations. We are much more than that.
The coalition party which backed his candidacy was formed, Barrow said, "to ensure that we'll be one Gambia, one nation, one people".
Other high profile dignitaries across the African continent as well as other parts of the world that attended the ceremony include Presidents of Ivory coast, Alassane Ouattara, Ghana Nana Addo Dankwa Akufo-Addo.