Goode and Tomkins have been sidelined by shoulder and ankle injuries respectively and will miss Sunday's clash with the Barbarians at Twickenham and the trip to Uruguay and Argentina.
Uncapped Northampton backs Burrell and Myler will link up with England after Saturday's Aviva Premiership final against Leicester.
"Luther and Stephen have played well in the second half of the season and have a great opportunity to put a marker down for the future on this tour," said England head coach Stuart Lancaster.
Goode and Tomkins were pencilled in to play against the Barbarians following Saracens' elimination from the Premiership play-offs.
"Our commiserations go to Alex Goode and Joel Tomkins," added Lancaster. "It's disappointing that they have to miss out but they've had excellent seasons and I'm sure they'll be back in contention next season."
Nine tourists are appearing in Saturday's final between Leicester and Northampton, so Lancaster has called up Exeter scrum-half Haydn Thomas and Sale lock Kearnan Myall to assist in the build-up to the Barbarians.
"It's good to have Haydn and Kearnan involved in the senior England environment ahead of what should be a great game against a very strong Barbarians team," said Lancaster.
"They have both played well recently and deserve this opportunity."