Lindblom was born in Skeda in Östergötland, son of a clergyman. He received his secondary education at Linköping gymnasium and matriculated at Uppsala University in 1763. In Uppsala he became student of the philologist Johan Ihre and the latinist Petrus Ekerman (who was also inspector of the Ostrogothian Nation).
He worked as a tutor for a noble family in Livonia 1764-1766, came back to Uppsala where he completed his magister degree in 1770. After having worked as a docent and a librarian at the university library, he became an extraordinary professor in 1779 and was appointed to the Skyttean professorship of Eloquence and Political Science in 1781, after the death of his teacher Johan Ihre. Lindblom published a History of Roman Literature (Illustriores linguæ Romanæ critici) and collaborated with Ihre on a Lexicon Latino-Svecanum, which he was eventually to complete in 1790. He published prolifically historical, literary and other topics, but is not regarded as particularly original in his scholarly production.
Lindblom was a favorite of Gustavus III, who made him bishop of Linköping in december 1786, in spite of the fact that he wasn't even ordained, a situation remedied a few days after the appointment. As bishop he succeeded Uno von Troil, who had been made archbishop, and in 1805 he succeeded von Troil as archbishop of Uppsala as well, an appointment which also made him Pro-Chancellor of the University.