Kathryn Abbate, who was paid more than $1 million as the head of the Miami Beach Community Health Center, told a federal judge Wednesday that she pleaded guilty to take “personal responsibility” for stealing $6 million from the federally funded facility for the poor and uninsured.

Abbate, who served as the center’s chief executive officer over the past decade, faces up to 10 years in prison when she is sentenced by U.S. District Judge Marcia Cooke on May 29.

But because she is cooperating with the U.S. attorney’s office in the ongoing embezzlement investigation, Abbate is likely to receive a sentence of about four years for her theft conviction. Abbate, 64, of Hollywood, who was arrested by federal agents last month, remains free on a $150,000 bond.

Parallel state charges are expected to be dropped against her, with certain conditions.

Abbate was fired last summer after outside auditors uncovered her fraud at the center, at 710 Alton Rd. and two other sites, and its board accused her of diverting $6.8 million for her personal use.

The center, with 300 employees, receives about $4 million in federal grants and Medicaid reimbursements annually. In 2011, the center received about $15 million from various county funds, including the Children’s Trust, AIDS programs and Jackson Health System.

Abbate “caused’’ the center to disburse 837 checks totaling $3 million made payable to her for “community development” between 2007 and 2012, said Assistant U.S. Attorney Michael Berger, who cited facts attached to her plea agreement. Each check was written in amounts of $5,000 or less, with Abbate providing no backup documentation, such as an invoice or receipt.

Abbate also carried out a cover-up. In 2012, she showed records to the center’s auditors that “fraudulently” indicated $1 million of the missing funds were paid to five doctors, according to the factual statement. In fact, “the money had not been paid to these doctors, but rather had been misappropriated by Abbate.”

The Miami-Dade state attorney’s office charges — one count of organized scheme to defraud and one count of first-degree grand theft — focused on Abbate’s cover-up of the $1 million involving the five doctors. The funds were supposed to be payments to the University of Miami Miller School of Medicine, but UM never received the money.

Abbate also “caused’’ the center to pay her $3 million in unauthorized compensation, such as unaccrued vacation pay, between 2008 and 2012, according to the factual statement signed by Abbate and her lawyer, Bruce Lyons.

Abbate’s misdeeds go back to 2008, when she was paid $824,000 — several times what other Miami-area clinic heads earned. In a Miami Herald story about her sky-high salary in 2010, Abbate said her base salary was $275,000 and the rest was buying out “my pension and vacation time.” She told The Herald she needed additional money because “I had a sick child.’’

In 2009, federal tax reports show, Abbate’s total compensation was $987,902, rising to $1.2 million in 2010. By contrast, the chief executive of Community Health of South Florida, with operations in South Miami-Dade and twice the revenues of Abbate’s center, received $265,000 in 2008.

After Abbate’s surrender in February, U.S. Attorney Wifredo A. Ferrer said: “We will not relent in our efforts to charge individuals who use the health care system to line their own pockets. Our investigation remains ongoing.”

Abbate’s sentence would ultimately depend on the extent of her cooperation with Ferrer’s office and agents from the FBI and the U.S. Department of Health and Human Services.

The Miami Beach Community Health Center released a statement praising the “strong action” of the U.S. attorney’s office because it “closes a sad chapter.”

“From the time Ms. Abbate’s outrageous breach of a sacred trust came to light, the center has cooperated fully with the U.S. attorney’s office,” the statement said.