The 33-year-old Mexican has now "accepted the mandatory fight" against Nottingham's Wood for the WBA (Super) featherweight title.
In April, the WBA ordered a fight between Santa Cruz and Wood, but there were no significant developments until it emerged earlier this week that a unification bout against WBC champion Rey Vargas was being pursued by the fellow Mexican.
The WBA denied this request and instead ordered him to face Wood next. He was only given 24 hours to answer and if he refused, he would have been stripped of his belt.
The WBA announced via their official Twitter account on Wednesday night that Santa Cruz and his team are taking the Wood fight:
"Leo Santa Cruz's team contacted the WBA Championships Committee and indicated that he will accept the mandatory fight against Leigh Wood. More information coming soon."
Promoter Eddie Hearn has campaigned for Wood to be upgraded to super champion for months given Santa Cruz's inactivity.
The Mexican defeated Carl Frampton via majority decision at the start of 2017 to reclaim his WBA (Super) belt.
The 33-year-old has made two successful defences, with the last coming in February 2019 against Rafael Rivera.
'El Terremoto' then stepped up to super featherweight. After besting Miguel Flores for the vacant WBA (Super) world super featherweight title, he was beaten by Gervonta Davis towards the end of 2020.
Santa Cruz returned to the ring earlier this year in a winning effort at super featherweight against Keenan Carbajal.
Wood meanwhile upset the odds to beat Xu Can for his WBA (Regular) featherweight last summer at Matchroom Headquarters during Fight Camp.
'Leigh-thal' then successfully defended his belt against Michael Conlan in a fight of the year contender in March at Nottingham's Motorpoint Arena.
Speaking to IFL's Kugan Cassius, Wood reiterated that he wants to battle Santa Cruz next:
"For me, it is a no-brainer [to face Santa Cruz]. To get upgraded, a unification fight or to rematch Conlan for more money.
"It is history. It's not going to change, I've already beaten [Conlan]. Money is irrelevant. Everybody needs it and hopefully after boxing, I've made enough to have the freedom to come and go as I please, and set my kids up, Which I'm on my way to doing as well.
"For me, history is more important. Winning them belts, beating them names. And that Conlan rematch will be there. He's got an ego so he wants to try and put that right, which he is not going to. But if they are going pay a lot of money to let him try, so be it."