Deals to bring Phil Bardsley and Mame Biram Diouf to the Britannia Stadium have already been agreed, with the pair leaving Sunderland and Hannover respectively.
Bardsley will add useful experience and competition for places in defence, while former Manchester United and Blackburn Rovers striker Diouf is a proven goalscorer.
Shawcross expects both to be useful additions to the ranks, with Stoke having pulled off quite a coup in securing the pair on free transfers.
He told The Sentinel: “They are good signings all round.
“They are free signings, so no gambles there, and they are both very good players with a good history.
“They will hopefully add to our squad and improve us. And I’m sure we will add a few more.”
Shawcross hopes the fresh faces will help Stoke to remain on an upward curve, with a top-half finish secured in the Premier League under the guidance of Mark Hughes in 2013/14.
He added: “We always want to improve on the previous year.
“I’m sure we will want to beat ninth, and our cup runs in the last couple of years haven’t been great, so we want to improve on that and get to some finals.”
Shawcross has also praised Hughes for the impact he has made at Stoke, with team spirit maintained while adding a sprinkling of creativity and attacking flair.
The defender said: “We had that spirit for six or seven years and our new manager acknowledged that, continued to use the same players and added some flair players.
“It’s a great combination, and we played some very entertaining football towards the end of the year.
“Overall, we had a few dips, but we finished with our highest-ever finish.”