Johann's younger brother Ignaz Heinrich von Wessenberg later chose an ecclesiastical career and in 1801 was appointed Vicar general of the Bishopric of Constance.

From 1801 he worked as a secretary at the Austrian embassy in Berlin led by Count Johann Philipp von Stadion and in 1805 was appointed ambassador at Kassel, where he witnessed the occupation by the French troops under General Mortier in 1806.

King Frederick William III had fled from Napoleon's forces to East Prussia and Wessenberg had no opportunity to convince him to join the Fifth Coalition against France.

From 1811 to 1813 on he led the legation at Munich and afterwards travelled as special envoy to London, France and Milan before in 1814 he was appointed second Austrian delegate (after Prince Metternich) at the Congress of Vienna.

After the Revolutions of 1848, retired Wessenberg was appointed Minister President on 18 July, he nevertheless was forced to flee with the court from the Vienna Uprising to Olomouc, whereafter he resigned on 21 November in favour of Prince Felix of Schwarzenberg.