The Bulgarian champions, only the country's second club to reach the group stages after Levski Sofia in 2006, did not disclose the length of the contract.
Ludogorets were forced to seek reinforcements after substitute keeper Ivan Cvorovic sustained a shoulder injury on Thursday.
Regular starter Vladislav Stoyanov is suspended after being sent off in the shootout win over Steaua Bucharest in the second leg of the playoff round.
"I hope we'll beat Liverpool," Borjan, 26, told reporters on Saturday.
"We have to be positive. There's no way for us going there, thinking about defeat," added the player, who was born in the former Yugoslavia and left Turkish club Sivasspor this year as a free agent.
The Eagles, who won three successive domestic league titles despite being based in the town of Razgrad with a population of less than 35,000, also face holders Real Madrid and Swiss champions Basel in their group.
Borjan, who has also played in Uruguay, Argentina, Serbia and Romania, has made 19 appearances for Canada since his international debut in 2011.
(Reporting by Angel Krasimirov, editing by Alan Baldwin)
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