The Swedish Damallsvenskan side confirmed the signing of the midfielder, who starred in Nigeria's 2018 Africa Women Cup of Nations title triumph in Ghana from Elitettan outfit Asarums IF.
Before her move to the elite division side, Ayinde helped Asarums to safety in the second division, scoring four goals, seven assists in 22 appearances.
Reacting to her signing, club's head coach Magnus Karlsson expressed joy over the capture of the 23-year-old, whose contract runs through till December 2019, with an option of an extension.
"We've been watching Ayinde since she came to Asarum and it's an interesting one player," Karlsson told club website.
"We have seen her in a couple of matches and met her on two occasions as part of the recruitment process. She has good speed and good technique.
"She can play in multiple places but is best in an offensive role in the midfield or in the attack.
"[Ngozi] Okobi and Ayinde have played together in both club teams (Delta Queens) and national team and know each other well."
On her own part, the former FC Minsk of Belarus midfielder said: "I was not thinking very long when Eskilstuna United offered a contract.
"It is a top club like Ngozi (Okobi) has spoken very well of. I will try to contribute with hard work and hopefully some goals."
The former Delta Queens star was part of Nigeria's campaign at the Women's World Cup at Canada 2015 and became a three-time winner of the Africa Women's Nations Cup at Ghana 2018.