After graduating from The Ohio State University College of Veterinary Medicine in June 1985, Linnehan entered private veterinary practice and was later accepted to a two-year joint internship in zoo animal medicine and comparative pathology at the Baltimore Zoo and Johns Hopkins University.

After completing his internship, Linnehan was commissioned as a captain in the U.S. Army Veterinary Corps and reported for duty in early 1989 at the Naval Ocean Systems Center, San Diego, California, as chief clinical veterinarian for the U.S. Navy’s Marine Mammal Program.

In 2008, he was the lead spacewalker on [(STS-123)] 1JA, an ISS assembly mission where he performed three EVAs and supervised the remaining two during the installation of the JEM module and Canadian SPDM.

During the 16-day flight the seven-person crew aboard Space Shuttle Columbia served as both experimental subjects and operators for 26 individual life science experiments focusing on the effects of microgravity on the brain and nervous system.

The crew of STS-109 successfully upgraded the Hubble Space Telescope's systems over the course of five consecutive EVAs, leaving it with a new power control unit, improved solar arrays, the new Advanced Camera for Surveys (ACS), and an experimental refrigeration unit for cooling the dormant Near Infrared Camera and Multi-Object Spectrometer (NICMOS).

The mission delivered the Japanese Logistics Module and the Canadian Special Purpose Dexterous Manipulator to the International Space Station.