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Parling, 31, has won 21 international caps, and played all three Tests for the British & Irish Lions in 2013.
Woodburn, 23, has scored 11 tries since making his Bath debut four years ago.
"We've slowly looked to add quality and experience to the squad since coming into the Premiership and that's what Geoff does," said coach Rob Baxter.
"There's no secret that this season we have looked a bit light in the second-row department and Geoff is a proven international performer."
Parling started his career with Newcastle Falcons before joining Leicester in 2009.
He has been part of a Tigers squad that won the Premiership in 2010 and 2013, as well as the Anglo-Welsh Cup in 2012.
"He adds great experience in running things like the line-out, has good leadership experience and all those things add up to it being a very good signing for us," added Baxter.
"I'm expecting him to have a very positive influence on and off the pitch in how he helps the team prepare for big games."
Woodburn, meanwhile, is on the less experienced end of the scale, having spent some of last season out on loan at Championship side Nottingham.
"With  we knew we had to recruit some players in the back three and Olly is a good age with decent Premiership experience," said Baxter.
Exeter Chiefs have signed England lock Geoff Parling from Leicester Tigers and Bath wing Olly Woodburn for next season on two-year contracts.