Simpson, 23, told BBC Radio Cambridgeshire: "Gary was looking at the team and the crop of players that he was given.
"We had a chat at the end of the season and he told me I was in his plans."
Johnson is the fourth manager that Simpson, 23, has played under at London Road, despite only joining Posh from Histon in October 2009.
He made 21 appearances last season, scoring twice in a 4-4 draw with Cardiff in December.
Simpson said it was a relief to discover the new manager wants to keep him.
"Whenever a new manager comes in you want to try and impress and be in his plans," he said.
Simpson has been used in a variety of midfield roles since arriving at Posh, but prefers to play just behind the front two.
"I like to bomb on from central midfield, so just behind the striker like I played at Histon is ideal for me," he said.
Meanwhile, physiotherapist Keith Oakes has left the club by mutual consent. He only signed a new four-year deal at London Road in 2009.
Source: BBC Sport
Source: BBC Sport