The charges against Patricia Cornejo, 39, of Los Angeles, carry the allegation that she took the child "with the intent to permanently deprive the parent and legal guardian custody."
Bail was recommended at $500,000, with arraignment expected Thursday afternoon.
Prosecutors offered no motive for the crime. Police have said they are unsure why it occurred.
Cornejo has four children of her own and no criminal record. If convicted, she faces a maximum prison sentence of 13 years.
Police said Cornejo told them she took Jessica from the playground area of the city's Echo Park on Sunday evening. She said she brought her to a free medical clinic Tuesday after the child complained of a sore throat.
She was arrested there when receptionist Denise Leon recognized Jessica from a picture authorities had circulated and called police.
Jessica and her parents met with the clinic staff on Thursday and offered their gratitude.
"Thanks to everyone and a kiss to all," Jessica said in Spanish. Dressed in a bright pink T-shirt, denim shorts and brand new Winnie-the-Pooh sneakers, she kissed her hand and waved it at the crowd.
A tearful Leon held the laughing child for several minutes.
"She'll always be a part of my life even after this dies down. I'll always love her," Leon said.
Jessica's father, Rafael Cortez, 38, also offered his thanks to everyone.
"If it wasn't for you, I don't know where my daughter would have ended up," he said in Spanish.
Cortez later said his wife, Maria Hernandez, would now remain at home with their four children rather than working with him at their taco cart in the park. He has changed the name of the business from "Smoke in Your Eyes Tacos" to "Happy Tacos."
Authorities have asked the parents not to discuss details of the kidnapping.
Police were unsure why Jessica had been taken. Several of Cornejo's neighbors in South Central Los Angeles appeared equally dismayed.
"It's a surprise to me," said Grace Baker, a neighbor of Cornejo's mother.
Neighbors said Cornejo sometimes lived with her children in an apartment behind her mother's home.
Her two daughters were placed in protective custody following her arrest, Police Chief Martin Pomeroy said, adding her two sons live with their father. He was not identified.
Jessica's family noticed her missing from the park, on the northwest edge of downtown, on Sunday evening. On Monday night, they issued a composite drawing of a man witnesses said they saw talking to Jessica in the park.
Police are still looking for the man but only as a witness, Pomeroy said.
They now believe the friendly child walked away with her abductor.
"I don't believe there was great force used and perhaps nothing more complicated than this woman held hands with Jessica and walked her out of the park," Pomeroy said.