Burley, who resigned as the manager of Third Division Colchester United on Christmas Eve after serving only six months of a two-year contract, described the job as a "dream".
But Ipswich could now face a possible £500,000 compensation claim from Colchester for the loss of Burley. The Essex club have already turned down two offers from the Premiership side, including one of £100,000.
Paul Goddard, the caretaker-manager since the resignation of John Lyall a fortnight ago, picked the team for last night's game but Burley will take over in time for the visit to Everton on Saturday.
The Ipswich chairman, John Kerr, is convinced Burley is the right man for the job.
He said: "George's record speaks for itself. He gained management and coaching experience in the hard school north of the border. His determination and the clear view of what he can do for this club shone through at his interviews."
Burley becomes only Ipswich's ninth post-war manager. He made 500 appearances for the Suffolk club after joining them as a youth player in 1971, winning 11 Scottish caps in that time, as well as picking up FA Cup and Uefa Cup-winning medals with the EastAnglian club under Bobby Robson.
He later played for Sunderland and Gillingham before returning to his native Scotland, where he was player-manager at Ayr, before two coaching spells at Motherwell.
Burley said: "It is a dream come true for me. Since the day I left Ipswich, I've been looking to get into the coaching and managing side of the game."
Burley is confident he can turn the club's fortunes around. "We haven't got millions to spend, so there is no easy route. It is going to be down to hard work by myself and the skill of the players. In my five or six years as a manager and coach, I have not had money to spend, so I'm used to making do with the players available."
Burley has yet to announce his backroom staff, although Dale Roberts, the caretaker at Colchester and another former Ipswich player, is a candidate to join him. Goddard is set to return to a coaching role.
East Anglia's other Premiership club, Norwich City, are looking abroad for a replacement for goalkeeper Bryan Gunn, who will miss the rest of the season. Yesterday Gunn had an operation on the right ankle he broke and dislocated at Nottingham Forest on Tuesday.
With 19-year-old Andy Marshall, whose substitute appearance at the City Ground was his Premiership debut, their only fit professional goalkeeper, Norwich desperately need reinforcements with two important Cup games to follow the holiday programme.
Negotiations began yesterday with a European club and Norwich are hopeful of sealing a signing before the weekend. They are also investigating the possibility of taking an experienced goalkeeper on loan.
Gerry Francis, the Tottenham manager, has decided against accepting a one-year, roll-over contract. Instead Francis, who refused to sign a long-term contract at his former club, Queen's Park Rangers, will continue at White Hart Lane on a month-to-month basis and then review the situation.
In Scotland, Arbroath have sacked their manager, George Mackie, after an eight-month reign. The Gayfield club are second from bottom of the Third Division and have not won a home league match all season.
The assistant manager, Jimmy Cant, will take over on a temporary basis and the club are to advertise for their 13th manager in 14 years.
Last night's football, page 31