Following the historic national polls last November, Ban congratulated Kyaw, elected by the Myanmar Parliament.
"He welcomes this as a significant achievement towards advancing the democratic reforms ushered in by the outgoing Government," a statement issued by Ban's spokesperson said.
"The Secretary-General hopes the people of Myanmar will continue steadfastly on the path of democracy and national reconciliation and, at this defining moment of transition, calls upon President-elect U Htin Kyaw, as well as all other significant stakeholders, to work inclusively towards a smooth and peaceful consolidation of unity and stability in the country," it added.
Suu Kyi's National League for Democracy party won a November 8 general election by a landslide, gaining an overwhelming majority in both houses of parliament.
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Kyaw will be sworn in on March 30 and replace Thein Sein, the retired general credited with guiding Myanmar out of junta rule as president of a quasi-civilian government that took over in 2011.
The world body has long been involved in Myanmar's transition after more than 50 years of military rule, appointing veteran Indian diplomat Vijay Nambiar as the Secretary-General's Special Adviser on Myanmar, a role he has held since 2010.