The 28-year-old has agreed terms with the Grecians having spent three seasons with Posh, during which time he accrued over 100 appearances.
The Austrian has also played for Falkirk, Torquay, Scunthorpe and York, and Exeter manager Paul Tisdale believes his acquisition is a sign of intent from the League Two club.
“Bobby is a goalkeeper at the perfect age – he has good experience and a very good pedigree,” Tisdale told the club’s official website.
“He comes in to compete and to raise the level of that department within our team, and we have got very high expectations of the quality that he’ll bring to the team.
“We have to try to build a team which is capable of moving up a level, and to get promoted you need players that are capable of performing to the top of the league and often to the league above. Bobby is one of those.
“I think it shows the intent we have at the moment. It is the first time in three or four years where we’ve had a summer where we’ve been able to look at recruiting players into the squad and raise the mean average of the performance levels.
“Bobby ticks so many boxes – he was high on our list and we’ve very pleased that we’ve persuaded him to come to Exeter.”