Raised in Livingston Parish, he began singing for family and friends at age three and sang in choirs and gospel quartets throughout his childhood and adolescence.

In late 1986 he returned to Louisiana where he performed in restaurants and bars until he met Cajun accordionist Steve Riley, with whom he formed the Mamou Playboys in 1988.

Greely appeared on albums released by Steve Riley and the Mamou Playboys, including the group's first eponymous album for Rounder Records (1990), followed by Tit Galop Pour Mamou (1992), Trace of Time (1993), Live (1994), La Toussaint (1995), Friday at Last (1996), Bayou Ruler (1998), Happytown (2000), Bon Rêve (2003), Dominos (2005), Live at New Orleans Jazz Fest (2008), and Grand Isle (2011).

As a member of the Mamou Playboys, Greely has been nominated for four Grammy Awards in the Traditional Folk, Zydeco and Cajun, and American Roots categories.

Since leaving the Mamou Playboys in the spring of 2011,[2] Greely has performed Cajun music worldwide in small acoustic formats, including solo, as well as with the GreelySavoyDuo (with Joel Savoy), GumboJet with Christopher Stafford and Jo Vidrine, and with a Blues/Cajun crossover group called Golden Triangle, with Johnny Nicholas and the Mamou Playboys' Sam Broussard.