Eriksson, 64, had met the club's board for seven hours on Tuesday before it was confirmed that he would work alongside coach Alexander Schmidt.
But 1860, who share the Allianz Arena with Bayern Munich but were relegated in 2004, said Friday that after a period of reflection, Eriksson had changed his mind.
The club's Jordanian investor Hasan Ismaik had wanted Erikkson appointed as head coach but a compromise was reached for the Swede to work with Schmidt, who took charge in November.
Eriksson had been working with Thai club Tero Sasana and his lengthy resume of former clubs includes Benfica, Roma, Fiorentina, Sampdoria, Lazio and Manchester City.
As well as having coached England, he has also managed the national teams of Mexico (2008-09) and Ivory Coast (2010).
Schmidt, 44, was previously the club's Under-21 coach and only took charge of the first team on November 17 after Reiner Maurer was sacked.
After 19 matches of the season, 1860 Munich are sixth in the table, five points off third place which would guarantee at least a promotion play-off spot.