Thanks for the correction. I also found that StringReplace works well too, about the same performance:

convertString[dateTime_]:=With[{ns=NumberString},
    StringReplace[{m:ns~~"/"~~d:ns~~"/"~~y:ns~~" "~~h:ns~~":"~~min:ns~~":"~~s:ns~~" "~~ampm:WordCharacter..:>
    "{"<>y<>","<>m<>","<>d<>","<>h<>Switch[ampm,"AM","","PM","+12"]<>","<>min<>","<>s<>"}"}]
    [dateTime]//ToExpression//DateObject
]

I optimized this some, instead of using If, Switch is a tiny bit faster. And instead of using StringRiffle, inserting the commas as strings with StringJoin gets the 20,000 timestamps converted in less than 0.6s

Genius! So not having the string in DateList form is the slowdown. It's only taking 0.8 seconds to do 20,000. Thank you!

Eric,

I get close to the same timing as Neil for his example. To simulate your format:

randomDateTime[years_, n_] := 
 With[{range = {UnixTime[] - years*365*24*60*60, UnixTime[]}}, 
  FromUnixTime /@ RandomInteger[range, n]]

dateStringFormat = {"Month", "/", "Day", "/", "Year", " ", "Hour12", ":", "Minute", ":", "Second", " ", "AMPM"};    

timeStamps = DateString[#, dateStringFormat] & /@ randomDateTime[5, 5000];

Block[{$DateStringFormat = dateStringFormat}, DateObject /@ timeStamps;] // AbsoluteTiming

(* {1.92389, Null} *)