The 26-year-old spent the 2014-15 campaign on loan at Elche, where he scored 14 league goals in 34 matches.
At the end of last season, the striker revealed that he would be leaving Elche this summer, despite having been expected to spend another season on loan at the recently-relegated Segunda Division club.
According to reports in Spain, Sociedad have paid £2m to acquire 50% of Jonathas's rights, with the other half belonging to Brazilian club Associacao Maga Esporte Clube.
"I feel very happy, so does my family, for signing for such a big club, with players at a high level and keen to do something important," he told the club's official website.
"It's a very exciting project. I come here to give everything to the team on the pitch. I come with great enthusiasm and that's important to perform on the field."
Jonathas had been previously linked with a move to Atletico Madrid.