Speculation surrounding Sigurdsson's future came to an end on Wednesday when Tottenham confirmed it had signed the 22-year-old on a reported five-year deal.
Sigurdsson had been linked with Swansea City, where he was on loan last season, and the midfielder confirmed there was also strong interest from Liverpool, which is now managed by former Swans boss
But Sigurdsson opted to move to White Hart Lane after a meeting with the Spurs' hierarchy, who persuaded him the north London club is destined for great things.
Spurs failed to make the UEFA Champions League last season after Chelsea's victory over Bayern Munich in the final, but Sigurdsson believes the club will be a serious challenger for a top-four place next term.
"I enjoyed playing under Brendan and I am grateful for everything he has done for me, but after careful consideration I liked Spurs best," Sigurdsson told Icelandic website mbl.is
"The team has world-class players in their ranks and they play good football, which I like.
"I was impressed with the club's plans for next season and the coming years.
"There is clearly great ambition at Tottenham and the club intends to do big things.
"It is a pleasure to see that
"There are top players in the team and the club is getting a new training ground."
Sigurdsson joined Swansea on loan from Hoffenheim last season and netted seven times in 19 appearances for the Welsh side.
Swansea had agreed a £6.8 million ($10.32 million) fee, and personal terms with the player, but Rodgers' departure to Liverpool scuppered the deal.
The midfielder has already spoken to
"I like him and the ideas he has," Sigurdsson added.
"He has faith in me and I'm looking forward to working under his leadership."
Sigurdsson's arrival has raised questions about the future of
The Spurs playmaker, who last year was the subject of a £40 million ($60.72 million) bid from Chelsea, has made it clear he wants to leave White Hart Lane, and Sigurdsson is being viewed by some as a like-for-like replacement.
Tottenham hopes to wrap up a deal for Ajax captain Jan Vertonghen in the near future and the club has also been linked with a move for Russian midfielder Alan Dzagoev.
English Premier League
Sunderland winger Adam Johnson is in favour of manager Paolo Di Canio's hardline approach to the job if it brings about an improvement in results.