The midfielder turned down a new contract at the Blues to move to the Keepmoat Stadium.
Academy graduate Close was offered a two-year deal by head coach Danny Cowley to remain at Fratton Park but instead penned a three-year contract with Rovers.
And after making 190 appearances for Pompey the 24-year-old Southsea lad – who is boss Richie Wellen’s first signing of the summer – said he was ready for his next challenge.
Close told Doncaster’s website: ‘I was offered the new deal but I just got to the stage in my career where a new challenge felt imminent for me. It felt like the natural next step in my career.
‘I always felt that leaving Pompey would be a bit of a shock but it felt natural and the next thing to do in my career.
‘To be the first signing is great for me and to be joining a club like Doncaster Rovers is a massive challenge for me and a really exciting one.
‘To have the manager show his interest and how much he wanted me was a big pulling factor and I can’t wait to get going for him.
‘It’s rare for a player to stay at one club for his whole career so it was something I was prepared for and something I knew was going to come along one day.
‘It’s a fair journey so it’s a big challenge and something I’m looking forward to.’
Close’s Pompey exit comes just three days after fellow Blues youth product Jack Whatmough completed his free-transfer move to Wigan.
The midfielder’s departure means Pompey currently have no senior central midfielders on their books, with Tom Naylor also on his way out.
Andy Cannon has also left after being named in the Blues’ released list at the end of the season.
According to some media outlets, Cowley has been linked with Perth Glory midfielder Brandon Wilson, who is a product of Burnley’s academy set-up.