The 52-year-old announced that she was leaving the USA job she had filled for five years on Saturday, after her team trounced Costa Rica 8-0 in a friendly.
Shortly afterwards, in Stockholm, the Swedish football federation announced that she would take over as national coach on 1 December, replacing Thomas Dennerby, who stood down from the post last month after the Olympics.
"We are enormously happy to reveal that Pia Sundhage will be our new national coach," federation president Karl-Erik Nilsson said.
Sundhage, who won 146 caps for her country between 1975 and 1996, said: "It is the realisation of a dream for me to become the national coach of my own country."
First up for Sundhage will be next year's European Championships, which Sweden is hosting, although she is expected to stay with the USA team for at least the next two matches of their victory tour, a pair of friendlies against Australia on 16 and 19 September.
The Americans then host two matches against two-time FIFA Women's World Cup champions Germany on 20 and 23 October.