Webster has teamed back up with former Northampton boss Gary Johnson at Huish Park after his contract with the Cobblers was terminated by mutual consent on Wednesday.
The 25-year-old becomes the second ex-Northampton player to be reunited with Johnson following Lewis Young's decision to sign for the Glovers earlier this week.
Webster arrived on loan at Sixfields from Doncaster in March 2011 before making the move permanent the following May. He made a total of 24 appearances for the Cobblers.
Stech has joined Webster in penning a two-year deal after he was released by newly promoted Premier League outfit West Ham.
It will be the 22-year-old Czech's second spell with Yeovil following a five-game loan stint last term, during which he kept a clean sheet and saved a penalty against Stevenage.