The 23-year-old goalkeeper is set to put pen to paper on a long-term deal that will make him one of the best-paid shot-stoppers in world football.
Henderson now looks set to compete with David de Gea to be United's first-choice goalkeeper next season.
He had spent the past two seasons on-loan at Sheffield United and wrote an Instagram message saying goodbye to the Yorkshire club - who have signed Aaron Ramsdale from Bournemouth as a replacement.
Henderson wrote: "I would like to thank the manager, my team-mates, the backroom staff and of course, the fans, who have been unbelievable towards to me.
"Winning promotion to the Premier League with my brothers and having the season we had this season is something I will never forget.
"I would like to thank the manager, my team-mates, the backroom staff and of course, the fans, who have been unbelievable towards me.
"I will look back at the last two years as an important chapter in my career and more than anything, I'm grateful to have had the opportunity to learn and develop with such a class group of lads.
"I can't wait for the next chapter! Once again, thank you for everything! Once a Blade, always a Blade!"
United boss Ole Gunnar Solskjaer recently said that he expects Henderson to "eventually end up as England and Manchester United number one."