Born in London, the son of a diamond merchant, he was educated at a Jewish school and studied philosophy and mathematics as well as botany at the University of London. He then studied law.
In 1847 he began to practice at Lincoln’s Inn, soon becoming eminent as a chancery lawyer. In 1865 he was made a queen’s counsel.
In 1868 Jessel entered Parliament as the Liberal member for Dover and in 1871 was appointed solicitor general in Gladstone’s administration, the first Jew to become a minister of the crown.
In 1873 Jessel was appointed master of the rolls, a post which gave him precedence after the lord chief justice, becoming the first Jew to wear the judicial ermine in England. He became president of the chancery division of the court of appeal, and was a member of the committee of judges making rules and procedures for the high court of justice and the court of appeal. From 1873 to 1883 he was head of the Patent Office.
He was active in the management of the University of London, of which he was vice-chancellor from 1880 until his death. He was a member of the royal commission which led to the Medical Act of 1886, the vice-president of the council of legal education and a fellow of the Royal Society.
Sir George was a good Hebrew scholar and his activities on behalf of the Jewish community included membership of the council of Jews' College from its inception in 1855 until 1863 and helping to draft its constitution. He was also a vice-president of the Anglo-Jewish Association.
Jessel was averse to writing, and during the years on the bench his powerful memory enabled him to dispense with notes and he usually delivered his judgment immediately at the end of a case. He advocated remodeling the bankruptcy law and criticized the English legal system, claiming that it should be based on Roman law.