Clever's directors together hold a 17% stake in the company.
The board, which have unanimously recommended shareholders accept the offer in the absence of a superior deal, said in a statement that a better proposal is neither present or expected.
BigAir made its takeover offer, for 0.35 shares and 1.82 cents cash for each Clever share, in November.
On Friday, BigAir revealed it had become a substantial shareholder in Clever with a total of 51,901 shares.
Clever owns fixed wireless networks in Melbourne, Sydney, Brisbane and Adelaide, providing services including internet, VPN and VoIP.
BigAir is a fixed WiMAX operator with coverage in Sydney, Melbourne, Brisbane, the Gold Coast, Adelaide and Perth.
The proposed merger between the two nearly went the other way. In January last year, Clever abandoned an attempt to acquire BigAir, after failing to receive enough acceptances.
CVA shares grew 3.9% in Wednesday's trading to $0.080.