Moyes officially replaced United's most successful manager Sir Alex Ferguson on Monday as the club embarks on a new era.
The former Everton boss confirmed Steve Round, Chris Woods and Jimmy Lumsden will form his coaching team.
And Woodward believes there is much to look forward to as the new regime embark upon defending the title.
"I believe with David and his new team in place, along with our current backroom staff, we can now start preparing for the new season ahead," said Woodward.
"This is an exciting and challenging time for the club and I have great belief that David and his team will have all the energy and attributes needed to help this club continue in its long-standing traditions."