Friday's announcement followed a seven-month criminal investigation into claims by Jose Orozco that Babeu threatened to have him deported if he revealed their relationship.
The investigation by Arizona Solicitor General Dave Cole found Babeu hadn't committed a crime, The Arizona Republic reported.
Babeu, who is running for re-election and won the Republican primary Tuesday, has denied Orozco's allegation. Babeu requested the investigation into the matter, the newspaper said.
Babeu had been a candidate for Congress and Arizona co-chairman of Mitt Romney's campaign for the Republican presidential nomination. He dropped out of the race for Congress in May, after Orozco's allegation was made public.
Babeu's relationship with Orozco was made public Feb.17 when the Phoenix New Times alleged the sheriff and his attorney, Chris DeRose, threatened to deport Orozco, who is from Mexico, if he revealed the relationship.
Babeu acknowledged Feb. 18 he is gay but denied abusing his position or threatening Orozco. He said the disclosure was meant to undermine him politically.