The 24-year-old former Brentford and Swindon man scored once in 46 league appearances in 2016-17.
He joins former Dons team-mate Dominic Poleon at the League One club after he moved to the Bantams last month.
Stuart McCall's side, who lost to Millwall in last season's play-off final, start their campaign with a home game with Blackpool on 5 August.
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The Nigeria international has been on loan at Qatari club Al Ain this season.
"I'm very happy and very excited that I'm here," 28-year-old Emenike told the club's website.
"I have always known West Ham as a great club. I have known [manager Slaven] Bilic for years and thank God we are here together."
Bilic previously managed Besiktas, based in Istanbul, Turkey - the city rivals of Fenerbahce.
Emenike, who has scored nine goals in 37 international appearances, becomes the club's second signing of the January transfer window, after Leeds defender Sam Byram.
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The former Sun and Daily Mail writer and sports editor for the Observer had been suffering from oesophagus cancer.
Mr Corrigan died on Thursday at a hospice in Penarth, Vale of Glamorgan, surrounded by his family, hours after watching his beloved Wales play England in Euro 2016.
His brother Chris, 69, said: "He could make you laugh in print, which not many people could do."
He added: "In every day life, he made people laugh - that's why he was so popular and that's how we'll remember him.
"Right up to the end, he always had a smile for the nurses."
Mr Corrigan was born and brought up in Roath Park, Cardiff, and had two brothers; Chris and Terry, 73, as well as son James and daughter Sally.
James Corrigan recently tweeted: "Just watched Wales win with my father in the hospice. At the whistle he said 'worth the wait' and went back to sleep. A lovely lovely moment."
Mr Corrigan co-wrote the autobiography of ex-Wales rugby star Jonathan Davies.
Mr Davies said: "Lost a very good friend today, RIP Peter Corrigan. Thank you for everything you did for me. I'll miss you."
He was also president of Glamorganshire Golf Club and was teaching his eight-year-old grandson Paddy how to play the sport he loved.
The club said: "The captains, officers and members of the club would like to extend their sympathy to Peter's family."
Mr Corrigan started his career at the South Wales Echo as a messenger when he was 16, working his way up before moving to London where he became a football writer for the Daily Herald.
He later moved on to cover golf and, after leaving the Observer in 1993, was appointed chief sports columnist for the Independent on Sunday and wrote The Hacker column, which he also published online.
Mr Corrigan said one story his brother was delighted with came when he bumped into Wales, Leeds United and Juventus legend John Charles on a beach while on holiday in Italy in the early 1960s.
"He said 'how you doing, Charlo?' and he said 'I'll give you an exclusive, I'm going back to Leeds.' It was a scoop he was very proud of."
Former editor of the Independent, Simon Kelner, said: "The world has lost a great man. Peter Corrigan, my friend, my mentor, died last night. He truly had bags of swank."
Ian Prior, the Guardian and Observer's current head of sport, tweeted: "RIP Peter Corrigan, former Observer sports ed. A wonderful writer, editor, and mentor to generations of journalists."
Bradford City have signed AFC Wimbledon midfielder Jake Reeves for an undisclosed fee on a three-year deal.
[NEXT_CONCEPT]
West Ham have signed Fenerbahce striker Emmanuel Emenike on loan, with an option to make the deal permanent at the end of the season.
[NEXT_CONCEPT]
Highly-respected sports journalist Peter Corrigan has died aged 80.