Huddersfield defender Murray Wallace has signed a new contract that will keep him at the club until the summer of 2017.
Nottingham Forest have signed Tom Ince on loan from Hull City on a deal until December 28.
The 22-year-old full-back is among those to have joined the Upton Park ranks, completing a season-long loan from capital rivals Arsenal.
He is still waiting on his first competitive appearance, with an unfortunate injury having delayed his bow.
Jenkinson has, however, been impressed by the work carried out by Sam Allardyce on and off the field in his absence.
Several high-profile additions have been made, with the likes of Mauro Zarate, Aaron Cresswell, Enner Valencia and Alex Song bringing added quality and competition for places.
Jenkinson told the club’s official website: “We’ve made some great signings and that was half the reason I joined.
“The club is clearly making a big push and we’ve signed some more players since I signed. I think that’s a real sign of intent.
“Hopefully the players we have brought in, along with myself, can do ourselves justice in a West Ham shirt.”
On former Arsenal colleague Song, he added: “He is a top player and West Ham have done very well to bring him in.
“Me, as much as the rest of the boys and the fans, are very excited to have him on board because he’ll bring an awful lot to the side.
“He hasn’t played regularly for a while now so he needs to get his fitness up as he has said, but when he’s firing on all cylinders he’ll be a fantastic player for West Ham, I’m sure.”
On his own fitness battles, with a hamstring problem having kept him out since the start of August, Jenkinson said: “Fingers crossed, I should be back for the next game.
“It seems like a long time out, but I have only missed three league games, so it’s not the end of the world. I’ll be back soon and hopefully I can do the business on the pitch.”