The 20-times top-flight champions meet Liverpool on Sunday and Solskjaer's future has been in doubt.
But Woodward said the former United striker was doing the right things required by the club.
"Ole's vision maps exactly to the core three football objectives we have," Woodward told the annual meeting for more than 400 Old Trafford employees.
Woodward said Solskjaer's effect on the young players at the club was particularly important.
"We must win trophies, we must play attacking football, and we must give youth its chance," he said.
"Last season we were the Premier League's leading club in terms of the most match minutes given to our own Academy graduates."
"We should all be proud that the significant investments we have made in our Academy - spanning recruitment, facilities and analytics - are now bearing fruit."
United last won the Premier League in 2013 and the club's fans are impatient for success.
But Woodward said Solsjkaer was working well, even if it was not showing in the club's results yet.
"Ole has also instilled the discipline back into an environment where we may have lacked it in recent years.
"He is building a squad that respects the club's history, in which players work hard and respect their team-mates. No-one is bigger than the club.
"The changes we saw over the summer have resulted in a very young squad. But it's also a squad, with the players and the culture, that provides a base camp for us to build and grow from as we start our new journey."
But Woodward said the former United striker was doing the right things required by the club.
"Ole's vision maps exactly to the core three football objectives we have," Woodward told the annual meeting for more than 400 Old Trafford employees.
Woodward said Solskjaer's effect on the young players at the club was particularly important.
"We must win trophies, we must play attacking football, and we must give youth its chance," he said.
"Last season we were the Premier League's leading club in terms of the most match minutes given to our own Academy graduates."
"We should all be proud that the significant investments we have made in our Academy - spanning recruitment, facilities and analytics - are now bearing fruit."
United last won the Premier League in 2013 and the club's fans are impatient for success.
But Woodward said Solsjkaer was working well, even if it was not showing in the club's results yet.
"Ole has also instilled the discipline back into an environment where we may have lacked it in recent years.
"He is building a squad that respects the club's history, in which players work hard and respect their team-mates. No-one is bigger than the club.
"The changes we saw over the summer have resulted in a very young squad. But it's also a squad, with the players and the culture, that provides a base camp for us to build and grow from as we start our new journey."