A person who wishes to apply for settlement (indefinite leave to remain) as an investor will need to meet the requirements in the Immigration Rules.
Depending on the level of investment in the UK, he or she must complete a continuous residence period of two, three or five years with no more than 180 days absence in any 12 calendar months. The person must show that they have maintained investments throughout the specified investment period. In addition, he or she must not have any unspent convictions within the meaning of the Rehabilitation of Offenders Act 1974, must not fall for refusal under the general grounds for refusal, must not be an illegal entrant, and must have a minimum of 75 points under the points-based system. The requirements to have sufficient knowledge of the English language and sufficient knowledge about life in the United Kingdom must also be met.
Further information can be found on the UK Border Agency website:
http://www.ukba.homeoffice.gov.uk/visas-immigration/working/tier1/oldinvestors/settlement/for those who entered in the previous investor route.
http://www.ukba.homeoffice.gov.uk/visas-immigration/working/tier1/investor/settlement/for those who are here as investors under tier 1 of the points-based system.