After being pieced together, the 18 primary mirror segments will work together as one large 21.3-foot mirror.
The full installation is expected to be complete early next year.
"The James Webb Space Telescope will be the premier astronomical observatory of the next decade," said John Grunsfeld, astronaut and associate administrator of the Science Mission Directorate at Nasa headquarters in Washington, DC, in a statement.
This first-mirror installation milestone symbolises all the new and specialised technology that was developed to enable the observatory to study the first stars and galaxies, provide answers to the evolution of our own solar system and make the next big steps in the search for life beyond Earth on exoplanets.
Several innovative technologies have been developed for the Webb Telescope which is targeted for launch in 2018.
Webb will study every phase in the history of our universe, including the cosmos' first luminous glows, the formation of solar systems capable of supporting life on planets like Earth, and the evolution of our own solar system.
The 18 separate segments unfold and adjust to shape after launch.
The mirrors are made of ultra-lightweight beryllium chosen for its thermal and mechanical properties at cryogenic temperatures.
Each segment also has a thin gold coating chosen for its ability to reflect infrared light.
The telescope's biggest feature is a tennis court sized five-layer sunshield that attenuates heat from the sun more than a million times.
The mirrors must remain precisely aligned in space in order for Webb to successfully carry out science investigations.
While operating at extraordinarily cold temperatures, the backplane must not move more than 38 nanometers, approximately one thousandth the diameter of a human hair.