Frederic Thomas Greenhalge was born in Clitheroe, Lancashire, England on July 19, 1842, to William Greenhalgh and Jane (Slater) Greenhalgh. He was the only son (of seven children). His father, the supervisor of a printing operation, was descended from the Greenhalghs, a family of longstanding note in Lancashire. The family moved first to Eshton and then Edenfield, where the young Greenhalge (who would change the spelling of his name as an adult) attended private school. In 1855 the family immigrated to Lowell, Massachusetts, where the father had been offered a job heading the printing department of the Merrimack Manufacturing Company.
Greenhalge attended the public schools of Lowell, where he excelled academically and participated in debating societies. In 1859, he enrolled in Harvard College, where he was a member of the Institute of 1770 and was well regarded as a debater. He left Harvard after three years because his father died, the family finances having suffered a setback due mill closures caused by the American Civil War. He briefly taught school in Chelmsford, Massachusetts and studied law. In 1863, he sought to enlist in the Union Army, but was rejected on account of poor health. He instead secured a civilian job work as a commissary for the army at New Bern, North Carolina. There he contracted malaria, and was sent home in April 1864. He resumed his study of the law, was admitted to the bar in Lowell in 1865.
On October 1, 1872, Greenhalge married Isabella (or Isabel) Nesmith, the daughter of John Nesmith, Lieutenant Governor of Massachusetts during the war. They had three children: Nesmith Greenhalge (1873–1874), Frederic B. Greenhalge (1875–?), and Harriet Nesmith Greenhalge (1878–?).
Greenhalge served on Lowell's common council in 1868 and 1869. He then became a member of the school committee in 1871, holding that post until 1873. In addition to his legal practice, he also served as a judge in the Lowell Police Court from 1874 to 1884. He was politically a reform-oriented Republican, but supported Horace Greeley in the 1872 presidential election. That year, he also ran unsuccessfully for the Massachusetts Senate as a Democrat.
Greenhalge was elected mayor of Lowell in 1880 and 1881 and was an unsuccessful candidate for election to the Massachusetts Senate in 1881. He was a delegate to the Republican National Convention in 1884 and a member of the Massachusetts House of Representatives in 1885 but was unsuccessful in his bid for reelection. He became city solicitor in 1888, practicing law in Middlesex and other counties. He was elected as a Republican to the Fifty-first Congress, serving from March 4, 1889 to March 3, 1891, but failed in 1890 to be re-elected to Congress, a casualty of that year's Democratic landslide.