The Argentine Tennis Federation decided against renewing Vazquez' contract after Argentina lost to Spain 3-1 in the 2011 Davis Cup final two weeks ago.
The 47-year-old Jaite will serve as captain in 2012 and 2013, with his fellow former ATP World Tour player Mariano Zabaleta serving as vice-captain. Jaite is a former top-10 performer on the ATP World Tour.
Argentina is a four-time Davis Cup runner-up and still seeking its first-ever championship. The Argentines also lost in the 1981, 2006 and 2008 finals, as they have been the bridesmaid three out of the last six years.