The Gunners are top of the Premier League and enjoyed wins over north London rivals Tottenham, as well as Sunderland, Stoke and Swansea last month.
Wenger’s team also made a winning start to their Champions League campaign and advanced in the Capital One Cup.
The awards double completes a remarkable recent turnaround for both player and manager.
Wenger was the subject of furious criticism from supporters following an opening day 3-1 home defeat to Aston Villa and the failure to make any significant additions to the squad in the transfer market.
The Arsenal Supporters’ Trust even questioned Wenger’s future at the club, saying contract talks to extend the Frenchman’s 17-year stay in north London should be put on hold.
However, the club record £42.4m signing of Germany playmaker Mesut Ozil appeased fans, while results on the pitch have further improved their mood.
Ramsey, meanwhile, was encouraged by former Wales striker John Hartson to leave Arsenal on loan in January in order to rediscover his best form after a succession of poor performances.
The 22-year-old midfielder did see out the season at the Emirates Stadium though, but scored only twice in 47 appearances.
But Ramsey has been integral to the Gunners’ strong early season form contributing eight goals in 11 games in all competitions, including five in September.