On January 31st 2006, Norwich replaced Dean Ashton with a new goalscorer on a permanent basis - Welsh international Robert Earnshaw from West Brom.The basic fee is £2.75m, with a further £750k based on various conditions, which could see the total rise to £3.5m, plus a 10% sell-on clause.

Robert began his career at Cardiff City and made his debut in the 1997/98 campaign. He was a prolific goalscorer scoring 84 goas in 178 appearances for the Ninian Park side. In is younger seasons, he had loans with Middlesborough (no appearances) and Morton (3 appearances, 2 goals). He joined Gary Megson's West Brom in August 2004 for £3m. He scored 17 goals in 24 starts for them during the 2004/5 Premiership campaign but fell out of favour with manager Bryan Robson during the 2005/6 season especially after Nathan Ellington joined from Wigan. At the date of signing, he has 23 international caps and has scored 9 international goals.

His full debut came on 5th February in the 2-1 defeat to Ipswich at Carrow Road.

A rich vein of scoring form saw the Football Rumours website link Rob with a £4million return to the Premiership if Portsmouth avoid relegation

On 27th May 2006, Earnie scored twice for Wales to give them a 2-1 win over World Cup finalists Trinidad and Tobago, in a game which Wales also fielded Carl Robinson and Simon Davies. This led to speculation on the Football Rumours website and on the Pink Un message boards on 29th May 2006 that Earnie was off to either Watford or Sheffield United. Both clubs are willing to pay £4.5 million for him but supposedly Watford are likely to get the striker however as they are prepared to offer £4.2 million + their 21 year old French striker Hameur Bouzazza. Speculation in the People on25th June 2006 suggested that Blackburn manager Mark Hughes might buy his compatriot Earnshaw to replace the Liverpool-bound Craig Bellamy.

Rob started the 2006/7 season well scoring against Preston, Luton, twice against Barnsley, twice against Southend and against Plymouth by the end of September 2006. However City's form slipped and Nigel Worthington was sacked on 2nd October 2006. Rob put the uncertainty of the managerial situation at Carrow Road behind him when he scored Wales' second in a 3-1 win over Cyprus on 11th October 2006, Jason Koumas and Craig Bellamy scoring the others.

With 17 goals scored for City by the beginning of January 2007, Earnshaw was undoubtedly linked by the media as a target for Premiership sides when the Transfer Window opened on 1st January 2007. Newcastle were said to be preparing a £6.5million bid before Christmas 2006 with Wigan and Middlesborough also reported to be watching Earnshaw. Portmsouth were then linked with Harry Redknap said to be preparing a £4million bid. Earnshaw's former Welsh manager Mark Hughes was the next to be linked with speculation of a £5million transfer. On 3rd Janaury 2007, Norwich dismissed speculation linking Premiership bottom placed side Watford with a move for Earnie.

Injuries ruled Earnie out of most of the second half of the 2006/7 season but he finished the campaign with 19 goals.

Linked to Watford and Charlton during May and June 2007, Rob signed for Derby County, newly promoted to the Premiership, for £3.5million on 29th June 2007 as the Rams exploited a minimum fee clause in Rob's contract.

Earnshaw however didn't settle well at Pride Park and scored just two goals during the season, and had not even commanded a regular first team place. In March 2008, he lost his place in the Welsh international squad. However that did not deter Glenn Roeder from making an attempt to bring Earnshaw back to Carrow Road on loan in mid-March. However, according to reports in the Midlands, Roeder's plans were blocked by Jewell "because it was not in Derby's best interests". Roeder instead signed Blackburn's Dutch Under-21 international Maceo Rigters on 19th March 2008 until the end of the season. Derby were relegated to the Championship on 29th March 2008

In May 2008, rumour had it that Norwich City, Notts Forest and Cardiff City were fighting it out to secure Earnshaw's signature for the 2008/9 season as Paul Jewell had indicated his willingness to listen to bids for the Welsh international. On 14th May 2008, it was reported that Earnshaw was in discussions with newly promoted Notts Forest over a £2.5million move to the City Ground, although Sheffield United were also said to be interested. Jewell added: "I think it's a fair price. It's a loss of £1.1m over a year but as I've said, I want to change things around quite drastically and everyone has a price."

Earnshaw signed for Notts Forest in May 2008 for £2.65m, signing a three year deal. He made his competitive debut in a 0–0 draw with Reading on 10 August 2008,[20] scoring his first competitive goals for Forest in their League Cup first-round tie at home to Morecambe, getting two on 13 August 2008. He finished the season with 17 goals in 34 appearances.

In August 2009, he was linked with a move to Newcastle United and Middlesbrough, ollowing the latter's sale of Robert Huth and Tuncay to Stoke City.

Out of contract at the end of the 2010/11 season, Rob was believed to be close to signing for Birmingham before the sensational departure of Blues boss Alex McLeish to Aston Villa. Earnshaw scored nine times in the Championship in 2010/11 and grew frustrated at the rotation policy adopted by Billy Davies as he juggled with so many options up front. Instead Earnshaw signed a two year deal with Malky Mackay's Cardiff on 6th July 2011