wright was educated at st andrew's university, halle and leiden. he was professor of arabic at university college london from 1855 to 1856, and professor of arabic at trinity college, dublin from 1856 to 1861. from 1861 to 1869 he was an assistant in the department of manuscripts at the british museum, and from 1869 to 1870 assistant keeper at the museum. in 1870 he was appointed sir thomas adams's professor of arabic at cambridge university, and he held the chair there until his death in 1889.