And Mulvihill has selected the Saints pair – who have more than 350 outings in black, green and gold and 73 international caps between them – in the 23-man squad.
Wood has not played since suffering a shoulder injury against Leicester Tigers back in February, but he will get one final game after announcing that he will retire this summer.
Tuala has also been an influential figure at Saints, but he will be heading home to New Zealand after his contract at the club expired.
Wood, Tuala and the rest of the Barbarians squad will assemble in Asturias ahead of the match at Estadio El Molinón in Gijón on Saturday (kick-off 9pm local time).
And John Spencer, president of Barbarian FC, said: “We are very much looking forward to this week as we prepare to face Spain on Saturday night.
"The club is buzzing after a wonderful victory over England on Sunday and this new squad, coached by John, are excited to take up the reigns and embody the Barbarians' ethos and playing style: spirit, passion, courage and flair, united by lifelong friendship.”
Barbarian FC squad to face Spain
Forwards: Ed Byrne (Ireland, Leinster), Scott Baldwin (Wales, Ospreys), Charlie Faumuina (New Zealand, Toulouse), Devin Toner (Ireland, Leinster), Steve Mafi (Tonga, Oyonnax), Rob Harley (Scotland, Glasgow), James Botham (Wales, Cardiff), Abraham Papali’i (Cannaught), Kirby Myhill (Wales, Cardiff), Wiehahn Herbst (Cell C Sharks), Scott Andrews (Wales, Cardiff), Joe Tekori (Samoa, Toulouse), Dan Baker (Wales, Dragons), Tom Wood (England, Saints)
Backs: Sebastian Bézy (France, ASM Clermont), Tim Nanai-Williams (Samoa, Toulouse), Seabelo Senatla (DHL Stormers), Hadleigh Parkes (c) (Wales, Panasonic Wild Knights), Rey Lee-Lo (Samoa, Cardiff), Adam Byrne (Ireland, Leinster), Rhyno Smith (Bennoton), Mathis Galthié (Colomiers), Ahsee Tuala (Samoa, Saints)