The 29-year-old, who collapsed while playing for Denmark at Euro 2020 last summer, was a free agent after leaving Inter Milan by mutual consent as rules in Italy prevented him from playing with a implantable cardioverter defibrillator (ICD) device fitted.
The ex-Tottenham midfielder had been training with former club Ajax but has now agreed terms with Brentford having completed his medical assessments.
Brentford boss Thomas Frank, who worked with Eriksen while in charge of Denmark's Under-17s squad early in his career, welcomed his compatriot to the club.
"We have taken an unbelievable opportunity to bring a world-class player to Brentford," Frank said. "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."
Brentford said Eriksen completed the details of his transfer from Amsterdam and will join up with the club in the coming days.
"I can't wait to get started and hopefully I'll seen you all very soon," Eriksen said in a short video on Brentford's website.
