Both players had been on trial with Kenny Shiels' side before the new year and have now committed to the club after sufficiently impressing the Derry boss.
Vemmelund, 23, is a former Denmark Under-19 international and arrives at the Brandywell following spells at Swedish side Brommapojkarna and Icelandic team Stjarnan.
The defender, who can also play in midfield, told the Derry Journal he is hopeful that playing with Derry City can aid him in his quest to earn a move to England.
“I honestly don’t know that much about the football here in Ireland," Vemmelund said. "But it’s a good option for me to improve my career.
"I have a dream to play in England so I think this is my best chance to get a move there eventually."
Delgado, meanwhile, comes to Derry City having previously played for Fontsanta Fatjo, in Group Three of the Segona Catalana - the sixth tier of Spanish football.
From Cornella in Barcelona, Delgado is a midfielder but can also play in defence, which Shiels identifies as an asset.
"[Delgado] is neat and tidy, [he] breaks the play up," said the Derry boss. "He’s got a good range of passing and he’s good in the air.
"He can play centre back when required as can Vemmelund which means we don’t have to go and get a fourth centre half.
"But I’m delighted to get both of them on board."
Meanwhile, Bohemians have confirmed that Dylan Hayes will remain at Dalymount Park for the 2016 season.
The 20-year-old joined the club from Athlone Town and made 12 league appearances for Keith Long's side in 2015.