The Republican governor scheduled a news conference for Wednesday on Penn State's campus in State College to announce the filing in U.S. District Court in Harrisburg.
The sanctions, agreed to by the university in July, included a $60 million fine that would be used nationally to finance child abuse prevention grants. State and federal lawmakers have raised objections to the money being spent outside Pennsylvania.
A message seeking comment on the expected lawsuit was left with the NCAA on Tuesday.
Last month, a Pennsylvania congressman said he was unhappy with how the NCAA responded to a request from the state's U.S. House delegation that the whole $60 million in Penn State fines be distributed to causes within the state.
NCAA president Mark Emmert had said in a Dec. 12 letter that a task force had been charged with allocating at least 25 percent of the fine money to programs in Pennsylvania.
Republican Rep. Charlie Dent said days later in a statement that Emmert's response was "unacceptable and unsatisfactory."
The NCAA said then that it stood by what Emmert said.
The fine was just part of college sports' governing body's sanctions on Penn State for its handling of the abuse scandal involving Sandusky, a former assistant under head football coach Joe Paterno.
Sandusky, a former defensive coordinator, was convicted in June on charges he sexually abused 10 boys, some on campus. The 68-year-old was sentenced to 30 to 60 years in state prison.
Eight young men testified against him, describing a range of abuse they said went from grooming and manipulation to fondling, oral sex and anal rape when they were boys.
Sandusky didn't testify at his trial but has maintained his innocence, acknowledging he showered with boys but insisting he never molested them.