The 24-year-old has signed a three-year deal with Rovers after successfully completing a medical.
With his deal at Pompey expiring at the end of June, Close had been offered fresh terms for the next two seasons by his hometown club, who were not in a position to take up an option of an extra season on his existing contract - which would have increased the player’s salary.
He has subsequently elected to head north and join Rovers, with Close well known to Doncaster assistant manager Noel Hunt, who was a team-mate at Fratton Park in 2016-17.
On joining the club, Close said: “I was offered the new (Portsmouth) 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."
Close came through the ranks at Pompey, making his debut as an 18-year-old in a 3-1 win over Yeovil in September 2014.
He has made 190 appearances for the south coast club, scoring 19 goals.
The experienced schemer helped the Blues claim the Checkatrade Trophy at Wembley in 2019, as well as successive League One play-off finishes in 2018-19 and 2019-20.
After spending the majority of the 2020-21 season in the cold under former manager Kenny Jackett, Close was brought firmly back into the fold after Danny Cowley took over in March.
The academy product started 10 of Cowley's 12 games in charge as Pompey narrowly missed out on the League One play-offs.