Dr. Graeme traveled to Philadelphia along with the newly appointed Lieutenant Governor of Pennsylvania, Sir William Keith. Keith and his entourage sailed into the city on May 31, 1717. There were age-old connections between the Keith's and the Graeme's. Anne Drummond was related to the Keith's by marriage. The Graeme's also sheltered William Keith's father and uncle after the Battle of Sheriff Muir, the decisive engagement between the forces of King George I and James Stuart. The Keiths sided with the losing Stuart side). Dr. Graeme made these connections more personal and immediate by marrying William Keith's step-daughter, Anne Diggs, in 1719.

Not much is known directly about Dr. Graeme's medical practice. From references made by his contemporaries, we can assume that he was a competent and respected physician. He served as Port Physician from 1727-1741, and he was a consulting physician to the Pennsylvania Hospital from its beginning. As Port Physician he instituted the practice of quarantine in order to deal with controlling the spread of epidemic sicknesses. The confines of the months-long crossing often increased the likelihood of contagious diseases. Dr. Graeme would inspect the incoming passengers, and then confine those who were sick, or in contact with the sick, until they were all healthy enough to enter the city. Because of the large influx of immigrants from Germany at that time, some of the sicknesses were named "Palantine Fevers" after the source of many of those newcomers.

Governor Keith appointed Graeme as Naval Officer in 1719, and as Register General, and Master of Chancery in 1724. He was a member of the Provincial Council from 1726 to 1738.

In tribute to his sense of fairness and character, Dr. Graeme was appointed to the Supreme Court of Pennsylvania in 1731 as the Third of the three judges. He was appointed Second Justice on the Court in 1738. He also served as "judge of oyer and terminer for the counties of Philadelphia, Bucks, and Chester."

In 1739 he purchased Fountain Low, Governor Keith's estate in Horsham. Keith had returned to England in 1728, leaving the lands in trusteeship for his wife, Lady Anne Keith, and family. Dr. Graeme was one of the trustees along with Thomas Sober and Patrick Graeme (Thomas' brother). The estate was sold in 1738 to Joseph Turner, and Turner transferred the property to Graeme in 1739.

Dr. Graeme renamed the estate "Graeme Park" and set about improving both the interiors and the surrounding grounds. He and his family used the estate as a summer home, residing in Society Hill in Carpenter's Mansion, on Chestnut Street, between Sixth & Seventh Streets in Philadelphia through the rest of the year.

As part of his improvements, Graeme installed Georgian panelling in the Parlor, the Master Bedchamber, and several other rooms, built an outdoor kitchen, and "grained" several of the chamber doors for effect. He also laid out a formal garden to the front of the mansion and established a 300 acre Deer Park to make it "a piece of Beauty and Ornament to a dwelling (that any English noble) would be proud to have...by his house." (Letter to Thomas Penn, 1755)

Because of a deterioration of his own health, and partly as a result of his wife's recent death, Dr. Graeme started to spend more and more time at Graeme Park after 1765. His youngest daughter, Elizabeth, took over the hostess' duties at both Graeme Park and the Society Hill house, maintaining the Graeme reputation for hospitality and grace. Elizabeth was a respected poet and the center of what was probably America's first "salon." Influential statesmen, writers, and musicians would gather frequently at the Graeme household in Philadelphia.

Graeme did not retire from society, however. He served as President of the St. Andrew's Society from its inception until his death in 1772. He was elected to the American Philosophical Society as well as the American Medical Society in 1768. His attendance at a Society dinner in 1771 was considered "the greatest honor" by one of the participants.

Dr. Graeme died of a heart attack while walking on the grounds at Graeme Park on September 4, 1772. The Rev. Dr. Smith described him as "blest with a clear head, a masculine understanding, and a happy sagacity which justly placed him for nearly half a century at the head of his profession." His funeral was attended by a "great concourse of respectable inhabitants of all denominations" testifying to the great esteem in which he was held by the citizens of Philadelphia.