Sale of West Brom to Chinese owners all but done
Former Blackburn chief executive John Williams will replace Peace, who has been chairman for 14 years.
"My immediate priorities will be to maintain the club's stable structure, respecting its well-run nature and its heritage," said Lai.
"I have no intention of changing the club's ethos."
He added: "I believe that we have a competitive team, with the right management and coaching staff in place."
Williams said his "immediate focus is on our activity in the transfer window" a day after the club pulled out of a move for West Ham striker Diafra Sakho.
"(Manager) Tony Pulis and (technical director) Nick Hammond have told the board we are two or three players short," he said.
"Realistic targets have been identified and there are funds available.
"We need to get them over the line to ensure Tony has a competitive squad for what is going to be a challenging and demanding campaign."
Lai, 42, oversaw the growth of landscaping company Palm in his home country before retiring in May 2014 to focus on private investment.
Palm, which was valued at £1.8bn on the Chinese stock exchange, has contributed to the takeover.
The deal was agreed in June and is dependent on approval from the Financial Conduct Authority and the Premier League.
West Brom came close to being sold to a Chinese consortium last summer before Peace, who owned 88% of the club, broke off negotiations.
It had been reported that Peace was looking for about £150m for his stake in the club, which recorded pre-tax profits of £7.6m in April.
He first invited offers of investment in June 2008.
"I believe this deal will enable Albion to build on the strong, sustainable foundations that have been the cornerstone of the club's progress," said Peace.
"The club can look to the future with excitement about the opportunities ahead."
Fellow Midlands clubs Aston Villa and Wolves have also been taken over by Chinese investors this summer.