"Drunken Sailor" AKA "Hooray an' Up She Rises," was reported in Olmstead, F. A., "Incidents of a Whaling Voyage," 1841, about a voyage in 1839-40. This was the first mention. Hugill says, "Sung by the Indiamen of the John Company." The chantey is probably English.

What tune was used at that time is not known.
Probably more than one tune was used over time. Stan Hugill is the source for the attribution to an Irish Dance (and march) tune, which he does not identify. See Hugill, "Shanties From the Seven Seas," 1961 and reprints.