The research firm said its purchasing managers index for December came in a 52.1, confirming a previously released flash estimate at a slightly higher growth rate than November when the PMI level was 51.7.
An index number above 50 indicates growth.
"The upturn in the eurozone private sector economy gained momentum in December. Although the recovery remains modest and frail overall, growth of output was nonetheless recorded throughout the second half of 2013," Markit said.
The firm said manufacturing "continued to lead the recovery in December," with the fastest pace of growth since May 2011. The service sector, concurrently, "increased further, although the pace of expansion remained modest and eased to a four-month low," in the final month of the year, Markit said.