Shares in the healthcare company jumped 34% to 825p as the fund managers agreed to the bid, which values BTG at 840p per share.
Woodford has long been a backer of the company, which floated on the stock market in 1995, investing through his Invesco Income (UK) and High Income (UK) funds, positions maintained by Barnett, his successor on the funds.
Woodford invested again when launching his Woodford Equity Income fund, with BTG a 1.8% position in his £5.1 billion portfolio.
Invesco is the company's biggest backer and between them, Invesco and Woodford own just under a third of the shares.
Both have given 'irrecvocable undertakings' to vote in favour of the takeover, as have BTG directors.
Woodford has maintained close links with BTG, whose chief executive Louise Makin sits on the board of the Woodford Patient Capital (WPCT) investment trust.
BTG featured in the WPCT at outset, though Woodford sold the shares from his investment trust in 2016.
The boost from the BTG takeover hands Woodford and Barnett some respite as both struggle with long-running performance issues.
The Woodford Equity Income and Invesco Income (UK) and High Income (UK) funds are grouped at the bottom of the Investment Association's UK All Companies sector over three years, down 9.8%, 3.2% and 1.6% respectively.
The BTG bid follows a couple of takeovers for Woodford stocks in the recent months, with biotech companies Abzena and Vernalis both taken over, although both were small positions in the Equity Income fund.
A private equity consortium meanwhile swooped on Woodford and Barnett holding CityFibre earlier in the year.