While many on the Street are becoming more bearish about recent weaknesses in global markets, one well-known market watcher says the bull run is just taking a break to celebrate its teenage years age. 

Bull Market Could Last Until 2038, When Millennials Peak

Tom Lee, head of research at Fundstrat Global Advisors and former J.P. Morgan chief equity strategist, spoke on CNBC's "Squawk Box" on Thursday, indicating that the market strength enjoyed by investors over the past ten years could last up to 20 more years. 

"It could last to 2035" or "2038," Lee stated. "That's going to coincide with millennials peaking."

As Lee put it, the U.S. market is "already growing a little mustache, so it's not a teenager anymore."

The Fundstrat co-founder wrote a note to clients on Wednesday flagging the bottom of the recent market sell-off and recommending that investors grab shares of beaten down players in industries like industrials, energy, materials, tech and consumer discretionary, while cycling out defensives. The market watcher's quant model highlighted 23 comeback stock candidates, including Home Depot Inc. (HD), Boeing Co. (BA) and Microsoft Corp. (MSFT). 

Lee is forecasting a 10% jump in equities by end-of-year, despite forecasts that more losses could lay ahead due to a "complete loss of confidence." 

In August, Lee spoke on CNBC's Trading Nation, forecasting bitcoin's value to be "explosively higher" by year-end, potentially reaching prices of $25,000. He attributed his prediction to a a correlation between the price of emerging market equities and bitcoin. 

Moving forward, the bull/bear debate on the Street wages on, with optimists like Lee downplaying risks of rising rates, slowing corporate earnings growth, and China-U.S. trade tensions. November has historically proved a bullish time of year for stocks, with the Dow, the S&P 500 and the tech-heavy Nasdaq all posting positive returns over the past five years.

In the CNBC segment, Lee said he expects the market to rally at least 13% over three months, citing strong fundamentals and a solid economic backdrop.