Elliott was born in 1886 in Woodstock, New York. He attended Cooper's Institute in New York City and received training at the New York City firm of Welch, Smith & Provost. Early in his career he helped design buildings for the Jamestown Exposition of 1907 in Norfolk, Virginia. At the age of 21, he moved to Tampa and formed a partnership with Bayard C. Bonfoey. They designed the Tampa YMCA (1909), Centro Asturiano (1914) and Tampa City Hall (1915).
The partnership was dissolved in 1917 and he then created the firm of M. Leo Elliott, Inc., Architects and Engineers. Elliott then designed the Italian Club (1917) and Cuban Club (1918) in Ybor City. In 1925, the firm was doing projects all over Florida, maintaining a St. Petersburg office. Carl Atkinson Sr. was manager of St. Petersburg office during the 1920s. During the peak of the land boom, the firm employed six structural engineers, forty-six draftsmen, and seventeen site inspectors. One of the firm's major projects in St. Petersburg includes the 1926 Ninth Street Bank and Trust designed in the Neoclassical Revival style.
Many of Elliott's notable projects in Tampa designed during this era remain on Davis Island, in downtown Tampa and Temple Terrace. Other important buildings in Tampa designed by Elliott include the Masonic Temple, the Scottish Rite Temple and the First National Bank. He also designed Sarasota High School. In 1946 the firm became Elliott & Fletcher. Elliott retired from practice in 1954 and died on August 18, 1967.