Defender Wood's contract had been due to expire in the summer, but his form this season has earned a one-year extension.
Wood is the Millers' longest-serving player, having joined in 2014. He cemented his place in Rotherham folklore with both goals in the 2-1 2017-18 League One play-off final win over Shrewsbury Town. The winner came shortly before half-time in extra-time.
The 34-year-old from Ossett has played 143 times for Rotherham, scoring 15 goals.
At 19 years-old, Spence is at the opposite end of the scale when it comes to experience.
The right-sided player only made his Championship debut in December, but his start against Blackburn Rovers was his 10th in the league.
He has committed himself for another two-and-a-half years.
Londoner Spence initially joined from Fulham in 2018 after impressing on trial.
“We’re delighted to get Djed tied down for a longer period,” said Boro's head coach Jonathan Woodgate. “He has done exceptionally well since he came into the team. He earned the right, and he knows he has to keep working hard.
“We speak a lot and he knows the standards he has set, the standards we expect, and that he has to keep listening, keep working, and keep improving. Djed is a great young talent.”
Hayden Coulson and Marcus Tavernier have both recently agreed new contracts at the Riverside.
“It’s important we keep our young talent,” said Woodgate. “These lads have all earned their opportunities and they have taken them. They are the future of this club, and they all understand the importance of working hard and developing themselves as players.”