Set 202 to win in just over a session, England completed their three-day run-out by reaching the target inside 35 overs.
Ollie Pope added to his first-innings century with 90 off 67 balls and Joe Root followed up his second-day failure by spending 75 minutes at the crease for 31.
Harry Brook, who was skittish in making only two in the first innings, was bowled by Will Jacks for 19 attempting a reverse-sweep. England were taken to victory by captain Ben Stokes and Jamie Smith.
Jacob Bethell earlier made 70 for the Lions, finding form too late to push for a place in the Test side. Future Test hopefuls Ben McKinney and Jordan Cox both made their second half-centuries of the match to allow the Lions to declare on 251-6.
Off-spinner Shoaib Bashir again struggled. After returning 1-68 from 12 overs bowling for the Lions on Friday, he came in for more punishment as part of the England attack on Saturday – conceding almost seven runs an over. He was outperformed by fellow off-spinner Jacks, who bowled Root with a beauty.
Realistically, the action on the field was overshadowed by the news off it.
The all-clear is a huge boost for Wood, one of the fastest bowlers to ever play for England, albeit in a 37-Test career that has been blighted by injuries.
He has not played a Test since August 2024 – first because of an elbow problem, then the knee injury.
Despite the long absence, England were keen for Wood to be in their XI for the first Test, alongside Jofra Archer, to hit Australia with pace on what is expected to be a lively surface at Optus Stadium.
The tourists hinted at their plans for the Ashes opener by naming five pace bowlers, including Wood and Archer, and no frontline spinner in their XI for the tour game against the Lions.
Now England will have to weigh up including Wood in their team for the first Test, and how it would affect the balance of their attack if he is not risked. Josh Tongue could be included as a like-for-like replacement, or England could turn to a spin option.
If Wood does not play in the first Test, there is the option to build his fitness in Lions fixtures.
The Lions meet a Cricket Australia XI at Lilac Hill at the same time as the first Test, then move on to a two-day pink-ball game against a Prime Minister’s XI in Canberra.
Meanwhile, leg-spinner Rehan Ahmed has been ruled out of the remainder of the Lions’ tour with a leg injury.
Ahmed missed out on selection for the Ashes squad when England preferred Jacks as their second spinner.
The 21-year-old will return to the UK but is expected to be fit to play for Hobart Hurricanes in the Big Bash League from next month.
