The 32-year-old midfielder has spent his entire career at Goodison Park and, after helping his side finish sixth in the Premier League last season, hopes the new additions will improve their performance in 2013-14.
New manager Roberto Martinez has already recruited four players, with his former Wigan charges Joel Robles, Antolin Alcaraz and Arouna Kone being joined by 19-year-old Barcelona attacker Gerard Deulofeu, who agreed a season-long loan deal.
"We’ve brought four new signings in already and it’s been impressive. There’s been a momentum with us so far," Osman told the club's official website.
"Now we’re all together and have got the rest of our international lads back, we’ve got our full squad and we can start to look forward even more.
"It’s about how quickly now we can all understand what the new manager wants and how he wants us to play. That’s different from being comfortable on the ball. We need to be comfortable in the mind as well."
Everton continue their build-up to the new campaign with a friendly against Blackburn Rovers on Saturday, before then heading to the United States to take part in the Champions Cup, which begins on July 31.