Free agents can be signed by a club at any time during the season if they were released by their previous club before the end of the transfer window.
"I've had a good week here and I've had a very good impression of the whole club and all the people here. It's not hard to fit in nicely here," the 33-year-old told Burnley's website.
"It seems like an honest place and a very hard-working place and I appreciate being a part of it... I am here to try and sharpen up the competition in the goalkeepers' department and we'll see what happens down the line."
Club captain Heaton dislocated his shoulder against Crystal Palace on Sept. 10 and had surgery last week.
Nick Pope came on as a substitute for Heaton in the 1-0 win over Palace and kept his place for the 1-1 Premier League draw at Liverpool last weekend and Tuesday's penalty shootout League Cup defeat by Leeds United.
"I have seen the first two games Nick has played and he's done very well. I have a lot of respect for that," Lindegaard said.
Burnley, who have started the season strongly with two wins and two draws in their first five games, host Premier League newcomers Huddersfield Town on Saturday.
(Reporting by Simon Jennings in Bengaluru, editing by Pritha Sarkar)
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