The defender, who has since become co-manager at German side Bayer Leverkusen, made 464 appearances for the Reds after joining from Dutch club Willem II in 1999.
Hyypia had a highly successful spell at Anfield, winning a host of European and domestic honours, before departing the club in 2009 for a new challenge in a player-coach role at Leverkusen.
"The day I signed my contract with Liverpool, that's one day I will never forget because Liverpool was my favourite team when I was younger and it was a dream come true," he told the BBC.
"I was there a long time and I had to leave friends there - it was a bit emotional.
"Now I think of my Liverpool career with joy, especially the fans - I always had a good relationship with Liverpool fans. I guess they saw I always tried my best on the pitch.
|20/1||Liverpool are 20/1 with Bet365 to finish in the Premier League top four
Hyypia retired from the game in 2011, but in May 2012 was handed the reins at Leverkusen alongside Sascha Lewandowski after a successful caretaker spell.
The pair have since guided the club to third place in the Bundesliga behind current leaders Bayern Munich and defending champions Borussia Dortmund, but Hyypia has admitted to finding management more difficult.
"As a player it's quite easy - this job is much more difficult," he added. "It's quite funny being on the other side now to see how much work you have to do with the team, outside of the team, and all the planning for the season, for pre-season, and for every training session.
"As a player you show up half an hour before training and somebody tells you what to do. Then you go to the shower and go home."
Hyypia played under Gerard Houllier and Rafa Benitez at Liverpool and revealed that it was the latter who taught him most as a coach.
"I haven't had a lot of managers and coaches in my career but from every one I tried to take the positive things," he said. "The negative things, I don't want to bring them into my coaching.
"If we are talking about football tactically, maybe I learned the most from Benitez. Tactically he was good and maybe I'd say I've learned the most from him."