The duo cost a reported ￡25 million.
Winger Victor Moses is at Anfield on a season-long loan after seeing his chances of first-team action at Chelsea plummet following the arrival of forwards Willian and Andre Schuerrle.
Liverpool sent striker Fabio Borini on a season-long loan to Sunderland, while another Italian, former Anfield leftback Andrea Dossena, joined the northeast club from SSC Napoli.
While raising money from the sale of Fellaini, Everton signed midfielder James McCarthy from Wigan Athletic for ￡13 million and brought in Chelsea striker Romelu Lukaku and Manchester City midfielder Gareth Barry on season-long loans.
New Manchester City manager Manuel Pellegrini was looking to offload Barry after spending more than ￡90 million rebuilding the 2011-2012 champions’ squad after the team ended last season without a trophy.
West Bromwich Albion added two forwards to their squad, with Victor Anichebe arriving from Everton in a deal worth up to ￡6 million and Stephane Sessegnon coming from Sunderland.
French midfielder Morgan Amalfitano is on board too after being recruited for the season from Olympique de Marseille.
A striker also left The Hawthorns, with Peter Odemwingie leaving for Premier League rivals Cardiff City for about ￡2 million.
Stoke City signed Austrian forward Marko Arnautovic from Werder Bremen, while Fulham brought Montenegro international defender Elsad Zverotic from Swiss side BSC Young Boys.