Barca have been negotiating with Christensen for months, who is out of contract with Chelsea and an economic option to improve the defence.
Journalist Nicolo Schira says there is a deal between both sides to make his arrival at Camp Nou official. The Danish centre back will sign on for three years plus one additional optional year, for six million euros a season.
Christensen, 25 and 1.88m tall, has played 150 games for Chelsea and 80 for Borussia Monchengladbach.
He has also played for his country 54 times.
In the Champions League final last season he played 51 minutes, coming on for Thiago Silva who was injured.