Heath, a winger, and Press, a striker, are two-time World Cup winners and have previously played their club soccer in Europe.
The 32-year-old Heath, who was shortlisted for the world player of the year award last year, was at Paris Saint-Germain in 2013 and '14. She has spent the past seven seasons with the Portland Thorns.
“I’m looking forward to the challenge of competing in England, playing with and against some of the best players in the world,” said Heath, who has played 168 times for the United States and was described as a “proven winner” by Man United manager Casey Stoney.
Press has played in Sweden with Göteborg FC and Tyresö FF, and has mostly recently been at Utah Royals. She has scored 58 goals in 138 appearance for the U.S. national team.
Earlier, England defender Alex Greenwood signed a three-year contract with Man City after one season in France, where she lifted the Women's Champions League trophy with Lyon.
Greenwood joins fellow England defender Lucy Bronze in moving to City from Lyon.
City has not won the Women’s Super League since 2016 but has recruited strongly for this season.
“This club has always impressed me with their success, how much importance they view the women's game with and the players they attract, and it's an environment I'm really looking forward to working in,” Greenwood said.
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