The 29-year-old joins the Bees having passed a medical assessment following the heart issue which saw him collapse during a Euro 2020 game for Denmark last summer.
Eriksen helped Inter Milan to the Serie A title last season, but was ultimately released by the Italian giants as a result of his heart issues.
The move sees Eriksen reunite with Brentford manager Thomas Frank, with the pair having previously worked together for the Denmark Under-17s side.
"I am looking forward to working with Christian again. It has been a while since I last coached him, and a lot has happened since then. Christian was 16 at the time and has become one of the best midfield players to appear in the Premier League. He has also won trophies all over Europe and become the star of the Danish national team," Frank told the club's official website.
"We have taken an unbelievable opportunity to bring a world class player to Brentford. He hasn't trained with a team for seven months but has done a lot of work on his own. He is fit but we will need to get him match fit and I am looking forward to seeing him work with the players and staff to get back towards his highest level.
"At his best, Christian has the ability to dictate games of football. He can find the right passes and is a goal threat. He also has very, very good set piece delivery, both from corners and direct free kicks. He is a player you can find with the ball, and he will come up with a solution to the problem in front of him. Christian will also bring experience of top level football to the club. I expect him to have an impact in the dressing room and at the training ground."
Brentford director of football Phil Giles added: "We first discussed the possibility of Christian joining Brentford when we heard that he would be leaving Inter. It is fantastic that he is now with us.
"Naturally the process of signing Christian was more elongated than most transfers. I understand that many people will have questions about the process. In order to respect Christian's medical confidentiality, we won't be going into any details.
"Brentford fans can rest assured that we have undertaken significant due diligence to ensure that Christian is in the best possible shape to return to competitive football. Now Christian has made the decision to sign for Brentford, all parties want to focus fully on football.
"We are sure that Christian will make a big impact at Brentford and on the Premier League between now and the end of the season."
Eriksen will not train with Brentford this week having only recently received his COVID-19 vaccination, and he is therefore not expected to make his debut for the Bees during Saturday's FA Cup tie with Everton.
The Denmark international made 305 appearances for Spurs during his time in North London, scoring 69 goals and creating a further 90.