"[Posh manager] Gary Johnson is well respected. The chance to work under him was something I couldn't turn down," he told BBC Radio Cambridgeshire.
Hibbert joined the Shrews from Preston in 2007 and has netted 30 goals in 111 league and cup appearances.
With manager Paul Simpson having just lost his job, Hibbert said it was the right time to move on.
"I've enjoyed every single minute at Shrewsbury, it's a good club and I did well, especially last season," he said.
"It was a tough decision to leave, but with us missing out on promotion it seemed like the right time to go."
Posh now have three strikers signed up for next season with Aaron Mclean and Craig Mackail-Smith already on the books.
Hibbert said he is looking forward to working with the pair given their record in previous seasons.
"Everyone in the lower leagues knows about Mclean and Mackail-Smith, they've scored a lot of goals in League Two and League One and hopefully I'll hit it off with them," he said.
"I'm a target man, but I'm not just a big lump, I can get about the pitch as well and get goals."
Source: BBC Sport
Source: BBC Sport