Former Nottingham Forest and Liverpool winger Anderson, 24, has signed a two-year deal at Portman Road, while Emmanuel-Thomas has put pen to paper on a two-year contract with City.
Anderson made 23 appearances in his one season at Ashton Gate, scoring three times, after joining the club from Forest in the summer of 2012.
He began his career as a trainee at Hull before spending three years at Liverpool, for whom he failed to make a first-team appearance.
Anderson had a loan spell at Swansea before joining Forest after an initial loan spell in June 2009 for £250,000.
Emmanuel-Thomas, 22, joins back up with City boss Sean O'Driscoll, who previously signed him on loan at Doncaster.
The Arsenal academy product has had loan spells at Blackpool, Doncaster and Cardiff before Ipswich paid in excess of £1million for him in July 2011.
Emmanuel-Thomas made 75 appearances for Ipswich, scoring nine goals.
Bristol City have also signed midfielder Scott Wagstaff, who had been with Charlton since the age of eight, but was released earlier this summer.
He made over 150 first-team appearances for the Addicks and had loan spells at Bournemouth, Northwich Victoria and Leyton Orient for whom he made seven appearances last season.