Rodgers had been tracking the defender for some time but could neither convince the Bundesliga giants to let him go nor find the right financial package.
However, a deal was pushed through on deadline day and the 24-year-old could come straight into the squad for tomorrow’s clash in Perth but more likely Wednesday’s home meeting with Hibs.
Rodgers said: “He is a player who has sacrificed his own wages and money to want to come here to play which shows a sign that he is hungry to get his career back on track again.
“He recognises this is a big club which gives him the opportunity to do that. It is a great attitude to start with and I look forward to working with him. It says everything in terms of wanting to get football and get playing.
“He is very quick, he is dynamic and he also gives us flexibility because he can play on both sides.
“We had tracked him a while back but we couldn’t get him. There was no hunger from them to want to do anything.
“Now, thankfully, the club has been able to do an agreement and the boy has made a sacrifice as well.”
Toljan, who has an American father and a Croatian mother, represented Germany at the 2016 Olympics and the 2017 Uefa Under-21 Championships.
Dortmund paid €7 million to Hoffenheim for his services in 2017 but he has not played at all this season, with coach Lucien Favre preferring Łukasz Piszczek or Achraf Hakimi in his position.
However, he is hungry to resurrect his career at Celtic, having been sold on the switch in a telephone conversation with Rodgers.
Toljan said: “The coach is a big factor when you move to a club and I had good conversations with Brendan Rodgers. I knew of him because he managed good clubs in the Premier League.
“We spoke on the phone and he told me what kind of club Celtic is and his idea of football and how he sees me helping the team.
“I had other options but the conversation with Brendan Rodgers was good and I decided to sign for Celtic.
“I’m looking forward to challenging Mikael Lustig. Right-back is my position. But it’s like everywhere. There are guys who want to play and I am no different.
“I think Celtic’s style suits me well. They play offensive football and score many goals, so this could be a good match for me. I have come here because I want playing time. It’s always frustrating when you are not playing, so I hope I can get regular football with Celtic.”
Toljan is one of four major window signings, joining Oliver Burke, Tim Weah and Vakhoun Issouf Bayo. But there was bad news for Rodgers yesterday when it emerged that attacking creator Tom Rogic requires knee surgery and will be missing for six weeks.
He is the latest in a string of players to sit out with Kieran Tierney, Filip Benkovic, Olivier Ntcham and Dedryck Boyata all sidelined.
Rodgers said: “Tom injured his hand at the Asian Cup and we had a plan for him to go to London for a scan.
“When he was down there, we got a scan on his knee and it ended up that the knee was the one.
“He’s done his lateral meniscus, so he needs an operation next week. That will put him out for about six weeks.”