Ally McCoist's side have jetted out Stateside for a four-game tour as the Light Blues step up their preparations for the new campaign.
Rangers play the first of their friendly fixtures against Ventura County Fusion tomorrow and will also face Sacramento Republic before heading to Canada for games against Victoria Highlanders and Ottawa Fury.
The trip across the Atlantic will give boss McCoist a chance to put his squad through their paces ahead of the big kick-off.
But McGregor admits it will be vital for team spirit as well as he and fellow new recruits Kris Boyd, Kenny Miller and Marius Zaliukas settle into life at the club.
He said: "It is a great opportunity to mix with different people and get different experiences from people and gel with the team.
"Hopefully by the time pre-season is done and dusted and the season starts we are a really firm unit and we are ready to go and win the Championship."
Kyle Hutton, meanwhile, is confident Rangers will be in prime physical shape for the Championship kick-off next month.
The countdown is on to the start of Scottish season and the Gers' first competitive clash against Hibernian on August 5 in the Petrofac Training Cup.
The champions have already spent several days in the Highlands this summer and midfielder Hutton reckons they will move on to the next level during their time across the Atlantic.
"Things will get a lot harder for us fitness-wise over the next couple of weeks," he told rangers.co.uk
"We're well into pre-season now and the games are starting to come thick and fast so we need to be switched on.
"Without being disrespectful to the teams we played when we went up to Brora earlier in the month, the American sides will give us a tougher challenge and we need that.
"As we get closer to the start of the season, we need the intensity to pick up and the boys are really looking forward to the tour matches in that respect.
"Pre-season is going well for us. Brora was good once again and North America should benefit us as well.
"We are in a good position at this stage and everyone is looking really fit thanks to Jim Henry and his staff.
"Drawing at Brora was a disappointment but the boys were excellent against Fulham the other day.
"We looked really sharp as a team and we enjoyed the match. Playing on a better surface made a big difference and we got to pass the ball about.
"That was encouraging and hopefully we will have the opportunity to play on more good pitches in America and Canada that allow us to keep progressing."