Originating from a cold front beneath an upper-level low, Epsilon formed on November 29 about 915 mi (1470 km) east of Bermuda, becoming the second tropical storm to do so in that area of the Atlantic within the span of a week.

Initially, the National Hurricane Center (NHC) forecast the storm to transition into an extratropical cyclone within five days, due to conditions unfavorable for significant intensification.

Stronger wind shear caused rapid weakening, and the storm could no longer be classified as a tropical cyclone late on December 8.

[2] On November 27, a surface storm with gale-force winds developed beneath an upper-level low pressure area, about 1150 mi (1850 km) east of Bermuda.

[4] It moved slowly westward, becoming better organized,[5] and by late that day resembled a subtropical cyclone; however, as it was still connected to the cold front, it could not have been classified as such.

[10] Instead, it turned toward the southwest and executed a cyclonic loop; the unexpected motion caused larger than normal errors in the extended track forecast.

[2] As it moved to the south, the storm crossed over an area of warmer water temperatures, and the NHC remarked that "just a modest increase in convection [would be] needed to make Epsilon a hurricane."

However, four computer models predicted an alternate scenario, and forecaster Stacy Stewart stated such transition would only occur "barring any southward motion over warmer water that would prolong both the lifetime of Epsilon and the 2005 Atlantic hurricane season.

[13] Despite moving over slightly cooler water temperatures, Epsilon attained hurricane status late on December 2, following the development of a well-defined eye 29 miles (46 km) in diameter.

[16] Despite moving into an area of cooler waters and generally unfavorable atmospheric conditions, Epsilon retained its hurricane status; the only entity supporting its intensity was its warm upper-level temperature.

[19] For several days, the intensity fluctuated in a narrow range,[2] and although Epsilon was briefly downgraded to tropical storm status on December 4,[20] the NHC assessed it as remaining a hurricane.

[2] Despite the cold water temperatures and unfavorable strong upper-level winds, Epsilon maintained its intensity, and the Geophysical Fluid Dynamics Laboratory (GFDL) model predicted it would remain a hurricane for nearly three days.

[25] However, late on December 7, an approaching trough began increasing wind shear over the system,[26] displacing the convection from the center and causing the eye to dissipate.

[2] The NHC issued their final advisory on Epsilon at 1500 UTC that day, after the cyclone consisted of a tight swirl of low clouds with no convection.