Born on 29 January 1957 in Kowala, Kielce County, Wojda entered the Pallottines in 1976 and was ordained a priest on 8 May 1983. He received a Licentiate from the Pontifical Gregorian University in 1986, and a PhD in 1989. From 1991, he served in a variety of roles in Congregation for the Evangelization of Peoples. He was appointed the Congregation's under-secretary on 24 July 2012.
On 7 July 2019, ahead of the LGBT march scheduled to take place on 20 July, Wojda issued a non possumus proclamation to be read in all churches in Białystok and the entire Podlaskie Voivodeship. He called pride marches "blasphemy against God". He described the march as organized "by a foreign initiative in Podlaskie land and community, an area which is deeply rooted in Christianity and concerned about the good of its own society, especially children". Following the march, Wojda condemned the violence that occurred at the march as incompatible with Christianity and urged believers to pray for "the family and its internal purity".
He cooperates with Orthodox bishop James (Kostiuczuk) participating in ecumenic services. 
- "Resignations and Appointments, 12.04.2017" (Press release). Holy See Press Office. 12 April 2017. Retrieved 23 August 2019.
- "Rinunce e Nomine, 24.07.2012" (Press release) (in Italian). Holy See Press Office. 24 July 2012. Retrieved 23 August 2019.
- "Ksiądz Arcybiskup dr Tadeusz Wojda" [Archbishop Tadeusz Wojda, Ph.D.]. Archdiocese of Białystok (in Polish). Retrieved 23 August 2019.
- "Arcybiskup Tadeusz Wojda SAC". Episcopal Conference of Poland (in Polish). Retrieved 23 August 2019.
- "Odezwa Abp. Tadeusza Wojdy ws. marszu LGBT w Białymstoku" [Appeal from Archbishop Tadeusz Wojda on the LGBT march in Bialystok]. Archdiocese of Białystok (in Polish). Retrieved 23 August 2019.
- "Anti-Gay Brutality in a Polish Town Blamed on Poisonous Propaganda". New York Times. 27 July 2019. Retrieved 23 August 2019.
- Rogowska, Gabriela (8 August 2019). "The Rainbow on Fire". Visegrad Insight.
- Dehnel, Jacek (28 July 2019). "The struggle for LGBT equality: Pride meets prejudice in Poland". The Guardian. Retrieved 23 August 2019.
- Abp Wojda w cerkwi: chrzest zaproszeniem na drogę sprawiedliwości