Hulk joins Zenit St Petersburg
Hulk, 26, joined Zenit from Porto and the 23-year-old Witsel moved from Portuguese rivals Benfica.
"It's now official. Both players had signed five-year deals," Zenit spokesman Dmitry Tsimmerman said.
A club source said Zenit had paid 40 million euros for each player.
Hulk helped Porto to win three Portuguese league titles and the 2011 Europa League trophy after joining from the Japanese J League in 2008.
Hulk and Witsel became Zenit's first major signings in the summer transfer window, which remains open in Russia for another week.
Zenit, drawn in Champions League Group C along with AC Milan, Anderlecht and Malaga, will be able to use both players in Europe's premier club competition.
"We were trying to sign them before the Sept. 3 deadline for the Champions League so they can play for us in that competition as well as the Russian league," Tsimmerman said.
Media reports also linked big-spending Zenit, backed by Russian energy giant Gazprom, with a $40 million bid for Manchester United's Portuguese striker Nani.
Tsimmerman declined to comment on Nani's possible transfer.