Ingesson, 45, was part of the Swedish side that came third in the 1994 World Cup, and replaces Jörgen Lennartsson who led Elfsborg to its sixth league title last year, the club said in a statement.
The former midfielder said he had recovered from a bone marrow cancer, plasma cell myeloma, which he had made public in 2009.
“My physical condition is good. A bit overweight, but free from cancer,” he told local newspaper Borås Tidning (BT).
In sixth place and with four more matches to play, the team have little hope left of retaining their league title. Nevertheless, the sudden sacking of Lennartsson took many players by surprise.
“I was shocked and don’t really know what to say,” defender Andreas Karström told BT when he arrived for training on Monday.
Elfsborg has qualified for the Europa League but the team suffered a crushing 4-0 defeat in their opening match against Austrian side Salzburg.