Tagoe, who has scored four goals in 22 internationals and helped Ghana reach the 2010 World Cup quarter-finals, joined Partizan on a six-month loan with the option of making a permanent move at the end of the season.
"The main reason I joined Partizan is because I need regular first team football and I believe this is a step forward in my career," said Tagoe, who made only 12 appearances for Hoffenheim since he joined in 2009.
"I heard a lot of good things about Partizan and I will be completely focused on winning trophies with the club, I have worked hard to stay in shape and I am looking forward to joining my new team mates in training," he added.
Vukic returns for his third spell with Partizan, where he won two league titles and one national cup from 2000-2003. He played only two games when he arrived on loan from Shakhtar Donetsk in 2006 but was confident he still had plenty to offer.
"I am delighted with my new return home, I want to show that I am still a good player and help Partizan retain the league title," said the 31-year old attacking midfielder, who scored six goals in 26 international appearances.
With Portuguese midfielder Almami Moreira and Brazilian striker Cleo seemingly on their way out, Partizan are also looking to sign Tagoe's compatriot Dominic Adiyiah on loan from Italian league leaders AC Milan.
Adiyiah, who was the top scorer at the Under-20 World Cup in 2009 when Ghana won the title, is currently on loan at Italian second division side Reggina and Partizan president Dragan Djuric said he would be a natural strike partner to Tagoe.
"We have added two quality players to our squad and getting a third would leave us in the driving seat to retain the league and cup double," Djuric said.
Partizan are five points ahead of bitter city rivals Red Star at the December-February winter break and also meet them in the two-leg Serbian Cup semi-final in March and April.
