Woods has established a reputation as one of the finest players in the lower divisions and his talents have not gone unnoticed to the Hammers' scouting team.
The 21-year-old is wonderfully gifted technically, but his combative approach and energy means that he has become a key player for the Shrews, as they challenge for the League Two title.
Although Woods has little experience outside of lower leagues, he looks ready to make the step-up and West Ham are ready to give him the chance to fulfil his talent.
Impact on West Ham?
Whether Woods would have the ability to go straight into the Hammers starting line-up remains to be seen, but he certainly could develop into a key player for them in the future.
Woods is one of the most notable talents in the Football League and interest has been steadily rising in his signature.
West Ham have already shown that they are happy to give players in the lower divisions a chance by bringing in Aaron Cresswell, who has been hugely impressive since arriving from Ipswich Town last summer, and Woods would be hoping to follow in his footsteps.