West Ham will then have the option of a permanent deal to sign Carroll for an undisclosed fee at the end of the season.
"It's great to be here at West Ham and all signed up - I just can't wait to get started now," the 23-year-old Carroll told the official West Ham website.
"I want to be playing games and obviously hoping to score some goals. I know the manager well and some of the lads, so it is nice for me to come to a place where I know people."
Carroll, who scored a fine headed goal for England against Sweden at this year's European Championship, said the chance of working again with coach Sam Allardyce had been a key factor in his decision to join the Hammers.
"I'm hoping to add a lot of goals and create a few chances. I know Sam from Newcastle and he was a massive reason for me coming," he said.
"When I worked with him at Newcastle it was great so it was a no-brainer really."
"I think for all parties this is a great signing," he said.
"Andy is an all-round footballer, but because he is six foot three inches and one of his strengths is his aerial power, everybody dismisses the ability he possesses on the floor."
"I am really happy about this, it is my dream to play for Liverpool and I will give my all," German Yesil told the Liverpool website.
"The first thing is that I have to train and then in one or two years I hope, step by step, to be in the first team.
"I will work hard here. I have read how the manager here will make a team that is young and that makes many passes, and I think I can be the right player for this."
