Terrors boss Jackie McNamara, who has brought in eight new signings already this summer, believes the duo will bring a lot to his side ahead of the new SPL season
Centre-back Butcher has signed a two-year deal with the Scottish Premier League outfit, while striker Oyenuga will be under contract until May 2016.
Butcher, 22, has English Football League experience under his belt following a loan spell at Barnet in 2009, while 20-year-old Oyenuga had a brief loan stint in the SPL with St Johnstone last year.
United manager Jackie McNamara was pleased to add the duo to his squad for the 2013-14 campaign.
"Both players will be excellent additions to the squad," he told the club's official website.
"They have similar schooling having both come through the ranks at Tottenham together and they are young, hungry, excellent footballers with something to prove.
"We have now brought in eight new faces over the summer and I am excited by what we can achieve this coming season. Calum is an aggressive centre-half who is also comfortable with the ball at his feet.
"He is at the right age for us to continue his development and he is someone who I will look to see make an impact over the course of the season.
"Kudus will excite our fans. He is quick, direct and always looking to score goals. He also has excellent body strength for a 20-year-old and I can see him having an immediate impact at the club."