"There are credible issues that need to be resolved," Cuomo said, adding "an immediate resolution does not now appear to be at hand."
During a conference call, Cuomo said he was appointing Judith S. Kaye, the former Chief Judge of New York, to lead the inquiries.
Cuomo called the matters "complex" and "weighty" made even more so because of political considerations. "I understand the political environment," Cuomo said, adding that he was acting out of a "zeal to ensure the public's confidence."
The attorney general was under political pressure to recuse himself from the investigations as he is widely said to be planning a run for governor in November.
Some said a Cuomo probe would be a conflict of interest.
A Marist College poll this week showed Cuomo's approval rating fell 13 points in two weeks as he began investigating Paterson, the Democratic governor who until recently was running for a full term and likely would have faced Cuomo in the primary.
Several polls showed New Yorkers preferred an independent prosecutor for the case, not Cuomo, who said the polls had no impact on his decision to use "an abundance of caution."
Cuomo was investigating Paterson's role in the case in which a woman accused a trusted Paterson adviser of roughing her up.
Last October, Sherr-una Booker accused Paterson confidante David Johnson of choking her, tearing off her Halloween costume and shoving her against a mirror. She filed a domestic violence complaint but never filed criminal charges.
Paterson has acknowledged that he, two staff members and a member of his state police security detail all talked to Booker before a scheduled family court hearing. He has said Booker called him and he only offered support but did not try to get her to drop her complaint or change her story.
Booker did not show up for the hearing, and the domestic violence complaint was dropped.
Last week, a public integrity commission accused Paterson of violating state ethics laws when he sought and obtained free Yankees tickets for the 2009 World Series and then may have lied about his intention to pay for them.
Judge Kaye, who will serve pro bono, will serve "until the matters are resolved." She has been working in private practice since her tenure as chief judge ended.
"I thank the Attorney General of the State of New York for entrusting me with this serious and important matter. I promise that the public will have a full, fair and independent accounting of the facts," she said in a written statement.