Liverpool were clear favourites to sign Sigurdsson because of the Iceland international's close relationship with Reds manager Brendan Rodgers, who managed him at Reading and Swansea.
Sigurdsson surprised many when he decided to join Spurs instead after they had an £8million bid accepted for the 23-year-old.
Sigurdsson says he moved to Tottenham because he was convinced the club's recent league finishes indicated that they were more likely to achieve success, and a quick glance at the Barclays Premier League table suggests he was right.
Tottenham sit third in the division, some 12 points in front of Liverpool, and the Londoners beat Inter Milan 3-0 last night to all but book their place in the last eight of the Europa League - a competition which Rodgers' men were eliminated from last month.
"It was hard to turn down Liverpool because I know Brendan," said Sigurdsson.
"It was more about that than any of the history Liverpool have.
"When Tottenham came in, I had seen how they were last year and in the previous two years.
"They finished fourth last year and were unlucky not to get Champions League football, and you could see tonight that this is a great club with fantastic players.
"I'm really pleased I made that choice. There are so many good players here and hopefully we can be in the Champions League next season."
When he made him his first signing, Villas-Boas hoped Sigurdsson would slot directly in to the number 10 role which was then occupied by Hamburg-bound Rafael van der Vaart.
The Iceland forward had excelled in a similar role for Swansea last term, scoring seven goals and providing many assists during a memorable year for Rodgers and the Welsh club.
But Sigurdsson initially struggled to make the same impact at White Hart Lane, and he admitted recently that he would have considered leaving the club had they accepted one of three bids Reading lodged for him on transfer deadline day.
Sigurdsson has found himself back in the first-team of late, however, thanks to a series of impressive performances, most notably against West Ham and Arsenal.
He scored and set one up in the club's Europa League win last night and he admits his confidence is growing by the minute.
"It's important for every player to get a run in the team," Sigurdsson said.
"You see Gareth Bale now, he's got a lot of confidence and he's scoring every game.
"I know he's got an unbelievable amount of talent but it's different when you've got confidence: you can do those things you wouldn't do without it. It's really important.
"I think (the Inter game) was my best game for Spurs. It is good to get two starts in a row and these are the games you want to play in.
"It was really important to get my first league goal (against West Ham). Now I've got my second European goal.
"It gave me a bit of a lift and hopefully we can continue that run and build on it."
Spurs never looked like coming away from last night's last-16 first leg tie with anything other than a comprehensive victory.
Given that man of the moment Bale is out for the second leg after being cautioned for diving, Sigurdsson knows his team-mates must not think they are already in the hat for the quarter-finals, however.
"They are a top Italian team, but we created a lot of chances and dominated the game," Sigurdsson said.
"But the job is not done. We have to make sure we get one or two away goals to make it really hard for them. We know they're really tough to beat at San Siro, so it's only half-time and we have to make sure we're ready for that when we come to that game."