The Iceland international spent the second half of the season on loan at the Liberty Stadium and scored seven goals in 18 Premier League matches.
Swansea stated their intention to strike a permanent deal for the 22-year-old, who also said he wanted to stay in South Wales, and have reached agreement with the player and his Bundesliga club.
Sigurdsson will now travel to Swansea to undergo a medical.
A club statement read: "The club are delighted to have agreed terms with both player and club following Sigurdsson's hugely successful loan spell last season."
Hoffenheim paid Reading £6m for Sigurdsson in 2010, but he struggled for first-team football in the first part of 2011/12 prior to his loan move.
Swansea have also denied reports regarding Rodgers and Liverpool's interest in the Swans boss.
"We would like to clarify the speculation in the press surrounding our manager Brendan Rodgers," the club said.
"We would like to confirm that there has been no contact from Liverpool and nothing has changed since our previous statement on the issue."