But Spurs won the race for Lucas' signature, with the midfielder having arrived from the French capital to undergo a medical with Mauricio Pochettino's side earlier this week.
"The most important thing is to play," Lucas told Spurs TV . "Here, I think it's a new challenge to show my talent, my quality.
"It's also a big club. The history of the club is very interesting. It's a pleasure for me to play for Tottenham."
Tottenham have now completed their first January deadline day signing since 2015, when they brought in Dele Alli from MK Dons.
Frozen out by the arrivals of Kylian Mbappe and Brazil team-mate Neymar, Lucas had not started any league games for PSG this season and featured in just six matches in all competitions.
Lucas will now hope a solid second half of the season with Tottenham helps him muscle a way back into Tite's Brazil plans, after spending almost two years in the international wilderness since his last cap in 2016.
But Lucas will have to wait to get back on the pitch as he is not be eligible for selection against Manchester United on Wednesday, having missed Tuesday's 12pm deadline.
"It's a big challenge for me, a new chapter in my life," Lucas said in a video posted on Twitter . "I'm so excited to play, to get to know the new stadium and the new fans. I'm sure we can do big things together. It's really a pleasure for me to be here."
Lucas joined PSG from Sao Paulo in January 2013 for a reported £38m and went on to win four league titles and make 229 appearances in all competitions, scoring 46 times and setting up 43.
Nilo Effori, one of the lawyers involved in the deal, believes Lucas now has the chance to get his career back on track in north London.
“Now in Tottenham, Lucas will have the best opportunity to resume his winning career. Mauricio Pochettino was very anxious about hiring him," Effori said.
"It is enough to play in the Premier League, which is the most competitive league in the world, and will also be available to play in the Champions League”.
PSG chairman and CEO Nasser Al-Khelaifi, meanwhile, thanked Lucas for his service to the club and said he "will always have a special place in the heart of our supporters."
“He always gave his very best to try and help the team win," Al-Khelaifi added. "Thanks to Paris Saint-Germain, he discovered elite European football and we shared all together so many unforgettable moments. I would like to thank him for the five years he played with the Paris Saint-Germain jersey.