The Sun says the defender's £10million move from Rangers takes the White Hart Lane club's January spending to £22m.
Right-back Hutton, 23, is moving to London after snubbing two previous offers from Spurs.
The Scot, 23, leaves for an initial £9m with a further £1m to be paid based on appearances.
Gers boss Walter Smith said: "I know Alan was not in too much of a rush to go anywhere.
"But as the weeks went on, he has decided it is the right time for him to leave. It's the type of offer we couldn't turn down."
Hutton links up with Jonathan Woodgate, who signed from Middlesbrough in a £10m deal.